Beurling-Lax type theorems and Cuntz relations
We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms...
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| Vydáno v: | Linear algebra and its applications Ročník 633; s. 152 - 212 |
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Elsevier Inc
15.01.2022
American Elsevier Company, Inc |
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| ISSN: | 0024-3795, 1873-1856 |
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| Abstract | We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given. |
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| AbstractList | We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given. |
| Author | Alpay, Daniel Schneider, Baruch Colombo, Fabrizio Sabadini, Irene |
| Author_xml | – sequence: 1 givenname: Daniel orcidid: 0000-0002-7612-3598 surname: Alpay fullname: Alpay, Daniel email: alpay@chapman.edu organization: Faculty of Mathematics, Physics, and Computation, Schmid College of Science and Technology, Chapman University, One University Drive Orange, CA 92866, USA – sequence: 2 givenname: Fabrizio surname: Colombo fullname: Colombo, Fabrizio email: fabrizio.colombo@polimi.it organization: Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy – sequence: 3 givenname: Irene orcidid: 0000-0002-9930-4308 surname: Sabadini fullname: Sabadini, Irene email: irene.sabadini@polimi.it organization: Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy – sequence: 4 givenname: Baruch surname: Schneider fullname: Schneider, Baruch email: baruch.schneider@osu.cz organization: University of Ostrava, Department of Mathematics, 30.dubna 22, 70200 Ostrava, Czech Republic |
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| Keywords | 30C10 Beurling-Lax theorem Structure theorems Cuntz relations Rational functions 47B32 de Branges-Rovnyak spaces Backward-shift operator |
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| References | Lev-Ari, Kailath (br0550) 1986; vol. 18 Alpay, Dym (br0120) 1986; vol. 18 Jorgensen (br0510) 2006; vol. 414 Fuhrmann (br0470) 1996 Lax, Phillips (br0540) 1989; vol. 26 Rovnyak (br0620) Vinnikov (br0650) 1998 Bratteli, Jorgensen (br0350) 1997; 28 Dym (br0410) 1989 Fricain, Mashreghi (br0460) 2016; vol. 21 Ball (br0250) 1975; 52 Kreĭn, Langer (br0530) 1973; 34 Alpay (br0030) 1998; 99 Alpay, Vinnikov (br0220) 2002; 189 Poggio, Girosi (br0610) 1990; 78 Alpay, Bolotnikov, Loubaton (br0080) 1996; 24 Alpay, Dym (br0110) 1984; 7 Alpay, Jorgensen, Lewkowicz, Volok (br0180) 2016; 61 Kreĭn, Langer (br0520) 1972 Freitag, Busam (br0440) 2006 de Branges, Rovnyak (br0330) 1966 Alpay, Pinhas, de Vinnikov (br0200) 2020; 373 Alpay (br0050) 2016 Alpay, Dijksma, Rovnyak, de Snoo (br0100) 1997; vol. 96 Livšic (br0560) 1979; 2 Rudin (br0630) 1982 Alpay, Dym (br0130) 1992; vol. 59 Dym, McKean (br0430) 1976 Jaccard (br0490) 1901; 37 Alpay, Bolotnikov, Dijksma, de Snoo (br0070) 1996; 136 Alpay, Yger (br0230) 2019; 19 Bart, Gohberg, Kaashoek, Ran (br0290) 2010; vol. 200 Chen, Ma, Zhang (br0370) 2009; 410 Nudelman (br0600) 1993; vol. 61 Stone (br0640) 1932 Dickinson, Delsarte, Genin, Kamp (br0390) 1985; 32 Alpay, Colombo, Sabadini (br0090) 2019; 91 Livšic (br0580) 1983; 6 de Branges (br0310) 1963; 106 Jorgensen (br0500) 2006; vol. 234 Berenstein, Gay, Vidras, Yger (br0300) 1993; vol. 114 Brodskiĭ (br0360) 1971; vol. 32 Alpay, Dym (br0140) 1993; 111 Livšic (br0570) 1973 Donoghue, Masani (br0400) 1983; 28 Alpay, Dym (br0240) 1990; 137/138 Alpay, Mills (br0190) 2003; 1 Alpay (br0010) 1986 Livšic (br0590) 1986; vol. 19 Alpay, Sabadini (br0210) 2017; 530 Dym (br0420) 1990; vol. 122 Bart, Gohberg, Kaashoek (br0280) 1979; vol. 1 Ball, Helton (br0270) 1983; 8 de Branges (br0320) 1972 Alpay, Jorgensen, Lewkowicz, Marziano (br0170) 2013 Alpay (br0040) 2015 Fricain, Mashreghi (br0450) 2016; vol. 20 Alpay (br0020) 1998; vol. 6 Alpay, Dym (br0150) 1996; 241 Horn, Johnson (br0480) 1994 Alpay, Jorgensen, Lewkowicz, Martziano (br0160) 2015; vol. 244 Alpay, Ball, Gohberg, Rodman (br0060) 1990; vol. 47 Ball, Bolotnikov (br0260) 2019; vol. 275 de Branges, Rovnyak (br0340) 1966 Cuntz (br0380) 1977; 57 Alpay (10.1016/j.laa.2021.10.008_br0150) 1996; 241 Livšic (10.1016/j.laa.2021.10.008_br0560) 1979; 2 Bart (10.1016/j.laa.2021.10.008_br0280) 1979; vol. 1 Alpay (10.1016/j.laa.2021.10.008_br0060) 1990; vol. 47 Alpay (10.1016/j.laa.2021.10.008_br0220) 2002; 189 Alpay (10.1016/j.laa.2021.10.008_br0090) 2019; 91 Alpay (10.1016/j.laa.2021.10.008_br0190) 2003; 1 Alpay (10.1016/j.laa.2021.10.008_br0120) 1986; vol. 18 Dym (10.1016/j.laa.2021.10.008_br0420) 1990; vol. 122 Fricain (10.1016/j.laa.2021.10.008_br0450) 2016; vol. 20 Horn (10.1016/j.laa.2021.10.008_br0480) 1994 Alpay (10.1016/j.laa.2021.10.008_br0100) 1997; vol. 96 Alpay (10.1016/j.laa.2021.10.008_br0030) 1998; 99 Dym (10.1016/j.laa.2021.10.008_br0410) 1989 Rovnyak (10.1016/j.laa.2021.10.008_br0620) Rudin (10.1016/j.laa.2021.10.008_br0630) 1982 Jorgensen (10.1016/j.laa.2021.10.008_br0500) 2006; vol. 234 Stone (10.1016/j.laa.2021.10.008_br0640) 1932 Alpay (10.1016/j.laa.2021.10.008_br0040) 2015 de Branges (10.1016/j.laa.2021.10.008_br0320) 1972 Alpay (10.1016/j.laa.2021.10.008_br0070) 1996; 136 Alpay (10.1016/j.laa.2021.10.008_br0180) 2016; 61 Vinnikov (10.1016/j.laa.2021.10.008_br0650) 1998 Ball (10.1016/j.laa.2021.10.008_br0260) 2019; vol. 275 Bart (10.1016/j.laa.2021.10.008_br0290) 2010; vol. 200 Nudelman (10.1016/j.laa.2021.10.008_br0600) 1993; vol. 61 Cuntz (10.1016/j.laa.2021.10.008_br0380) 1977; 57 Alpay (10.1016/j.laa.2021.10.008_br0010) 1986 Alpay (10.1016/j.laa.2021.10.008_br0110) 1984; 7 Alpay (10.1016/j.laa.2021.10.008_br0170) 2013 Fricain (10.1016/j.laa.2021.10.008_br0460) 2016; vol. 21 Alpay (10.1016/j.laa.2021.10.008_br0020) 1998; vol. 6 Dym (10.1016/j.laa.2021.10.008_br0430) 1976 Ball (10.1016/j.laa.2021.10.008_br0250) 1975; 52 Dickinson (10.1016/j.laa.2021.10.008_br0390) 1985; 32 Jaccard (10.1016/j.laa.2021.10.008_br0490) 1901; 37 de Branges (10.1016/j.laa.2021.10.008_br0330) 1966 de Branges (10.1016/j.laa.2021.10.008_br0340) 1966 Bratteli (10.1016/j.laa.2021.10.008_br0350) 1997; 28 Jorgensen (10.1016/j.laa.2021.10.008_br0510) 2006; vol. 414 Alpay (10.1016/j.laa.2021.10.008_br0200) 2020; 373 Kreĭn (10.1016/j.laa.2021.10.008_br0520) 1972 Alpay (10.1016/j.laa.2021.10.008_br0130) 1992; vol. 59 Alpay (10.1016/j.laa.2021.10.008_br0160) 2015; vol. 244 Alpay (10.1016/j.laa.2021.10.008_br0210) 2017; 530 Livšic (10.1016/j.laa.2021.10.008_br0590) 1986; vol. 19 de Branges (10.1016/j.laa.2021.10.008_br0310) 1963; 106 Alpay (10.1016/j.laa.2021.10.008_br0050) 2016 Berenstein (10.1016/j.laa.2021.10.008_br0300) 1993; vol. 114 Ball (10.1016/j.laa.2021.10.008_br0270) 1983; 8 Donoghue (10.1016/j.laa.2021.10.008_br0400) 1983; 28 Kreĭn (10.1016/j.laa.2021.10.008_br0530) 1973; 34 Lev-Ari (10.1016/j.laa.2021.10.008_br0550) 1986; vol. 18 Alpay (10.1016/j.laa.2021.10.008_br0140) 1993; 111 Brodskiĭ (10.1016/j.laa.2021.10.008_br0360) 1971; vol. 32 Chen (10.1016/j.laa.2021.10.008_br0370) 2009; 410 Alpay (10.1016/j.laa.2021.10.008_br0080) 1996; 24 Alpay (10.1016/j.laa.2021.10.008_br0240) 1990; 137/138 Fuhrmann (10.1016/j.laa.2021.10.008_br0470) 1996 Lax (10.1016/j.laa.2021.10.008_br0540) 1989; vol. 26 Livšic (10.1016/j.laa.2021.10.008_br0580) 1983; 6 Alpay (10.1016/j.laa.2021.10.008_br0230) 2019; 19 Freitag (10.1016/j.laa.2021.10.008_br0440) 2006 Livšic (10.1016/j.laa.2021.10.008_br0570) 1973 Poggio (10.1016/j.laa.2021.10.008_br0610) 1990; 78 |
| References_xml | – volume: 34 start-page: 191 year: 1973 end-page: 230 ident: br0530 article-title: Über die publication-title: Acta Sci. Math. – year: 2015 ident: br0040 article-title: An Advanced Complex Analysis Problem Book. Topological Vector Spaces, Functional Analysis, and Hilbert spaces of analytic functions – volume: vol. 20 year: 2016 ident: br0450 article-title: The Theory of publication-title: New Mathematical Monographs – year: 2016 ident: br0050 article-title: A Complex Analysis Problem Book – volume: 7 start-page: 589 year: 1984 end-page: 641 ident: br0110 article-title: Hilbert spaces of analytic functions, inverse scattering and operator models, I publication-title: Integral Equ. Oper. Theory – volume: 111 start-page: 1 year: 1993 end-page: 28 ident: br0140 article-title: On a new class of structured reproducing kernel Hilbert spaces publication-title: J. Funct. Anal. – volume: 189 start-page: 283 year: 2002 end-page: 324 ident: br0220 article-title: Finite dimensional de Branges spaces on Riemann surfaces publication-title: J. Funct. Anal. – volume: 99 start-page: 413 year: 1998 end-page: 422 ident: br0030 article-title: A structure theorem for reproducing kernel Pontryagin spaces publication-title: J. Comput. Appl. Math. – start-page: 353 year: 1972 end-page: 399 ident: br0520 article-title: Über die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume publication-title: Hilbert Space Operators and Operator Algebras – year: 1986 ident: br0010 article-title: Reproducing kernel Krein spaces of analytic functions and inverse scattering – volume: 137/138 start-page: 413 year: 1990 end-page: 451 ident: br0240 article-title: Structured invariant spaces of vector valued functions, sesquilinear forms, and a generalization of the Iohvidov laws publication-title: Linear Algebra Appl. – volume: 61 start-page: 42 year: 2016 end-page: 54 ident: br0180 article-title: A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions publication-title: Complex Var. Elliptic Equ. – volume: 57 start-page: 173 year: 1977 end-page: 185 ident: br0380 article-title: Simple publication-title: Commun. Math. Phys. – volume: vol. 61 start-page: 171 year: 1993 end-page: 188 ident: br0600 article-title: Some generalizations of classical interpolation problems publication-title: Operator Extensions, Interpolation of Functions and Related Topics – volume: 2 start-page: 264 year: 1979 end-page: 286 ident: br0560 article-title: The inverse problem for the characteristic functions of several commuting operators publication-title: Integral Equ. Oper. Theory – volume: 28 start-page: 382 year: 1997 end-page: 443 ident: br0350 article-title: Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale publication-title: Integral Equ. Oper. Theory – volume: 78 start-page: 1481 year: 1990 end-page: 1497 ident: br0610 article-title: Networks for approximation and learning publication-title: Proc. IEEE – volume: 32 start-page: 603 year: 1985 end-page: 605 ident: br0390 article-title: Minimal realizations of pseudo-positive and pseudo-bounded rational matrices publication-title: IEEE Trans. Circuits Syst. – volume: vol. 234 year: 2006 ident: br0500 article-title: Analysis and Probability: Wavelets, Signals, Fractals publication-title: Graduate Texts in Mathematics – year: 1972 ident: br0320 article-title: Espaces Hilbertiens de fonctions entières – year: 1973 ident: br0570 article-title: Operator Colligations, Waves, Open Systems publication-title: Transl. Math. Monog. AMS. – volume: 1 start-page: 107 year: 2003 end-page: 111 ident: br0190 article-title: A family of Hilbert spaces which are not reproducing kernel Hilbert spaces publication-title: J. Anal. Appl. – volume: 6 start-page: 250 year: 1983 end-page: 273 ident: br0580 article-title: Cayley–Hamilton theorem, vector bundles and divisors of commuting operators publication-title: Integral Equ. Oper. Theory – volume: vol. 59 start-page: 30 year: 1992 end-page: 77 ident: br0130 article-title: On reproducing kernel spaces, the Schur algorithm, and interpolation in a general class of domains publication-title: Operator Theory and Complex Analysis – volume: 37 start-page: 241 year: 1901 end-page: 272 ident: br0490 article-title: Distribution de la flore alpine dans le bassin des dranses et dans quelques régions voisines publication-title: Bull. Soc. Vaud. Sci. Nat. – volume: vol. 122 start-page: 427 year: 1990 end-page: 482 ident: br0420 article-title: On reproducing kernels and the continuous covariance extension problem publication-title: Analysis and Partial Differential Equations – volume: 91 start-page: 12 year: 2019 ident: br0090 article-title: The Fock space as a De Branges-Rovnyak space publication-title: Integral Equ. Oper. Theory – volume: vol. 47 start-page: 1 year: 1990 end-page: 60 ident: br0060 article-title: Realization and Factorization of Rational Matrix Functions with Symmetries publication-title: Operator Theory: Advances and Applications – volume: vol. 275 start-page: 1 year: 2019 end-page: 47 ident: br0260 article-title: Multiplicative Stieltjes functions and associated pairs of reproducing kernel Hilbert spaces publication-title: Linear Systems, Signal Processing and Hypercomplex Analysis – year: 1982 ident: br0630 article-title: Real and Complex Analysis – year: 2006 ident: br0440 article-title: Funktionentheorie 1 – volume: 530 start-page: 15 year: 2017 end-page: 46 ident: br0210 article-title: Beurling-Lax type theorems in the complex and quaternionic setting publication-title: Linear Algebra Appl. – volume: vol. 1 year: 1979 ident: br0280 article-title: Minimal Factorization of Matrix and Operator Functions publication-title: Operator Theory: Advances and Applications – volume: vol. 6 year: 1998 ident: br0020 article-title: Algorithme de Schur, espaces à noyau reproduisant et théorie des systèmes publication-title: Panoramas et Synthèses – volume: vol. 18 start-page: 89 year: 1986 end-page: 159 ident: br0120 article-title: On applications of reproducing kernel spaces to the Schur algorithm and rational publication-title: I. Schur methods in operator theory and signal processing – volume: vol. 26 year: 1989 ident: br0540 article-title: Scattering Theory publication-title: Pure and Applied Mathematics – volume: vol. 18 start-page: 301 year: 1986 end-page: 324 ident: br0550 article-title: Triangular factorisation of structured Hermitian matrices publication-title: I. Schur Methods in Operator Theory and Signal Processing – start-page: 445 year: 1998 end-page: 476 ident: br0650 article-title: Commuting operators and function theory on a Riemann surface publication-title: Holomorphic Spaces – volume: 24 start-page: 156 year: 1996 end-page: 178 ident: br0080 article-title: On tangential publication-title: Integral Equ. Oper. Theory – volume: vol. 244 start-page: 67 year: 2015 end-page: 87 ident: br0160 article-title: Infinite product representations for kernels and iterations of functions publication-title: Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes – volume: 28 start-page: 77 year: 1983 end-page: 80 ident: br0400 article-title: A class of invalid assertions concerning function Hilbert spaces publication-title: Bol. Soc. Mat. Mex. (2) – year: 1966 ident: br0340 article-title: Square Summable Power Series – volume: 241 start-page: 3 year: 1996 end-page: 84 ident: br0150 article-title: On a new class of realization formulas and their applications publication-title: Linear Algebra Appl. – volume: vol. 96 year: 1997 ident: br0100 article-title: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces publication-title: Operator Theory: Advances and Applications – year: 1976 ident: br0430 article-title: Gaussian Processes, Function Theory and the Inverse Spectral Problem – volume: vol. 114 year: 1993 ident: br0300 article-title: Residue Currents and Bezout Identities publication-title: Progress in Mathematics – start-page: 161 year: 2013 end-page: 182 ident: br0170 article-title: Representation formulas for Hardy space functions through the Cuntz relations and new interpolation problems publication-title: Multiscale Signal Analysis and Modeling – ident: br0620 article-title: Characterization of spaces – volume: vol. 414 start-page: 165 year: 2006 end-page: 188 ident: br0510 article-title: Certain representations of the Cuntz relations, and a question on wavelets decompositions publication-title: Operator Theory, Operator Algebras, and Applications – volume: 373 year: 2020 ident: br0200 article-title: Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem publication-title: Adv. Math. – volume: 106 start-page: 445 year: 1963 end-page: 468 ident: br0310 article-title: Some Hilbert spaces of analytic functions I publication-title: Trans. Am. Math. Soc. – year: 1989 ident: br0410 article-title: -contractive matrix functions, reproducing kernel Hilbert spaces and interpolation publication-title: Published for the Conference Board of the Mathematical Sciences – volume: vol. 32 year: 1971 ident: br0360 article-title: Triangular and Jordan Representations of Linear Operators publication-title: Translations of Mathematical Monographs – volume: 8 start-page: 107 year: 1983 end-page: 142 ident: br0270 article-title: A Beurling–Lax theorem for the Lie group publication-title: J. Oper. Theory – volume: 410 start-page: 2365 year: 2009 end-page: 2376 ident: br0370 article-title: On the similarity metric and the distance metric publication-title: Theor. Comput. Sci. – volume: vol. 19 start-page: 275 year: 1986 end-page: 279 ident: br0590 article-title: Commuting Nonselfadjoint Operators and Mappings of Vector Bundles on Algebraic Curves publication-title: Operator Theory: Advances and Applications – year: 1996 ident: br0470 article-title: A Polynomial Approach to Linear Algebra publication-title: Universitext – start-page: 295 year: 1966 end-page: 392 ident: br0330 article-title: Canonical models in quantum scattering theory publication-title: Perturbation Theory and Its Applications in Quantum Mechanics – volume: vol. 200 year: 2010 ident: br0290 article-title: A state space approach to canonical factorization with applications publication-title: Linear Operators and Linear Systems – year: 1932 ident: br0640 article-title: Linear Transformations in Hilbert Space – volume: 136 start-page: 39 year: 1996 end-page: 80 ident: br0070 article-title: On some operator colligations and associated reproducing kernel Pontryagin spaces publication-title: J. Funct. Anal. – volume: 19 start-page: 97 year: 2019 end-page: 115 ident: br0230 article-title: About a non-standard interpolation problem publication-title: Comput. Methods Funct. Theory – volume: 52 start-page: 235 year: 1975 end-page: 259 ident: br0250 article-title: Models for noncontractions publication-title: J. Math. Anal. Appl. – volume: vol. 21 year: 2016 ident: br0460 article-title: The Theory of publication-title: New Mathematical Monographs – year: 1994 ident: br0480 article-title: Topics in Matrix Analysis – volume: vol. 61 start-page: 171 year: 1993 ident: 10.1016/j.laa.2021.10.008_br0600 article-title: Some generalizations of classical interpolation problems – volume: 78 start-page: 1481 year: 1990 ident: 10.1016/j.laa.2021.10.008_br0610 article-title: Networks for approximation and learning publication-title: Proc. IEEE doi: 10.1109/5.58326 – ident: 10.1016/j.laa.2021.10.008_br0620 – volume: vol. 275 start-page: 1 year: 2019 ident: 10.1016/j.laa.2021.10.008_br0260 article-title: Multiplicative Stieltjes functions and associated pairs of reproducing kernel Hilbert spaces – year: 2016 ident: 10.1016/j.laa.2021.10.008_br0050 – volume: 2 start-page: 264 issue: 2 year: 1979 ident: 10.1016/j.laa.2021.10.008_br0560 article-title: The inverse problem for the characteristic functions of several commuting operators publication-title: Integral Equ. Oper. Theory doi: 10.1007/BF01682736 – volume: 99 start-page: 413 year: 1998 ident: 10.1016/j.laa.2021.10.008_br0030 article-title: A structure theorem for reproducing kernel Pontryagin spaces publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(98)00174-5 – volume: 241 start-page: 3 issue: 243 year: 1996 ident: 10.1016/j.laa.2021.10.008_br0150 article-title: On a new class of realization formulas and their applications publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(95)00602-8 – year: 1982 ident: 10.1016/j.laa.2021.10.008_br0630 – year: 1972 ident: 10.1016/j.laa.2021.10.008_br0320 – volume: vol. 32 year: 1971 ident: 10.1016/j.laa.2021.10.008_br0360 article-title: Triangular and Jordan Representations of Linear Operators – year: 1996 ident: 10.1016/j.laa.2021.10.008_br0470 article-title: A Polynomial Approach to Linear Algebra doi: 10.1007/978-1-4419-8734-1 – volume: vol. 59 start-page: 30 year: 1992 ident: 10.1016/j.laa.2021.10.008_br0130 article-title: On reproducing kernel spaces, the Schur algorithm, and interpolation in a general class of domains – volume: vol. 234 year: 2006 ident: 10.1016/j.laa.2021.10.008_br0500 article-title: Analysis and Probability: Wavelets, Signals, Fractals – year: 1976 ident: 10.1016/j.laa.2021.10.008_br0430 – volume: vol. 20 year: 2016 ident: 10.1016/j.laa.2021.10.008_br0450 article-title: The Theory of H(b) Spaces. Vol. 1 – volume: 136 start-page: 39 year: 1996 ident: 10.1016/j.laa.2021.10.008_br0070 article-title: On some operator colligations and associated reproducing kernel Pontryagin spaces publication-title: J. Funct. Anal. doi: 10.1006/jfan.1996.0021 – volume: 189 start-page: 283 issue: 2 year: 2002 ident: 10.1016/j.laa.2021.10.008_br0220 article-title: Finite dimensional de Branges spaces on Riemann surfaces publication-title: J. Funct. Anal. doi: 10.1006/jfan.2000.3623 – start-page: 353 year: 1972 ident: 10.1016/j.laa.2021.10.008_br0520 article-title: Über die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume Πk – volume: vol. 244 start-page: 67 year: 2015 ident: 10.1016/j.laa.2021.10.008_br0160 article-title: Infinite product representations for kernels and iterations of functions – volume: 106 start-page: 445 year: 1963 ident: 10.1016/j.laa.2021.10.008_br0310 article-title: Some Hilbert spaces of analytic functions I publication-title: Trans. Am. Math. Soc. – volume: vol. 47 start-page: 1 year: 1990 ident: 10.1016/j.laa.2021.10.008_br0060 article-title: Realization and Factorization of Rational Matrix Functions with Symmetries – volume: vol. 114 year: 1993 ident: 10.1016/j.laa.2021.10.008_br0300 article-title: Residue Currents and Bezout Identities – volume: vol. 122 start-page: 427 year: 1990 ident: 10.1016/j.laa.2021.10.008_br0420 article-title: On reproducing kernels and the continuous covariance extension problem – volume: 91 start-page: 12 issue: 6 year: 2019 ident: 10.1016/j.laa.2021.10.008_br0090 article-title: The Fock space as a De Branges-Rovnyak space publication-title: Integral Equ. Oper. Theory doi: 10.1007/s00020-019-2550-2 – volume: 7 start-page: 589 year: 1984 ident: 10.1016/j.laa.2021.10.008_br0110 article-title: Hilbert spaces of analytic functions, inverse scattering and operator models, I publication-title: Integral Equ. Oper. Theory doi: 10.1007/BF01195919 – volume: vol. 414 start-page: 165 year: 2006 ident: 10.1016/j.laa.2021.10.008_br0510 article-title: Certain representations of the Cuntz relations, and a question on wavelets decompositions – volume: 28 start-page: 382 issue: 4 year: 1997 ident: 10.1016/j.laa.2021.10.008_br0350 article-title: Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N publication-title: Integral Equ. Oper. Theory doi: 10.1007/BF01309155 – volume: vol. 1 year: 1979 ident: 10.1016/j.laa.2021.10.008_br0280 article-title: Minimal Factorization of Matrix and Operator Functions – volume: 52 start-page: 235 year: 1975 ident: 10.1016/j.laa.2021.10.008_br0250 article-title: Models for noncontractions publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(75)90093-1 – volume: 37 start-page: 241 year: 1901 ident: 10.1016/j.laa.2021.10.008_br0490 article-title: Distribution de la flore alpine dans le bassin des dranses et dans quelques régions voisines publication-title: Bull. Soc. Vaud. Sci. Nat. – start-page: 161 year: 2013 ident: 10.1016/j.laa.2021.10.008_br0170 article-title: Representation formulas for Hardy space functions through the Cuntz relations and new interpolation problems – volume: 34 start-page: 191 year: 1973 ident: 10.1016/j.laa.2021.10.008_br0530 article-title: Über die Q-Funktion eines π-hermiteschen Operators im Raume πκ publication-title: Acta Sci. Math. – volume: vol. 96 year: 1997 ident: 10.1016/j.laa.2021.10.008_br0100 article-title: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces – year: 1966 ident: 10.1016/j.laa.2021.10.008_br0340 – year: 2015 ident: 10.1016/j.laa.2021.10.008_br0040 – volume: 19 start-page: 97 issue: 1 year: 2019 ident: 10.1016/j.laa.2021.10.008_br0230 article-title: About a non-standard interpolation problem publication-title: Comput. Methods Funct. Theory doi: 10.1007/s40315-018-0255-1 – volume: 24 start-page: 156 year: 1996 ident: 10.1016/j.laa.2021.10.008_br0080 article-title: On tangential H2 interpolation with second order norm constraints publication-title: Integral Equ. Oper. Theory doi: 10.1007/BF01193458 – volume: vol. 6 year: 1998 ident: 10.1016/j.laa.2021.10.008_br0020 article-title: Algorithme de Schur, espaces à noyau reproduisant et théorie des systèmes – start-page: 295 year: 1966 ident: 10.1016/j.laa.2021.10.008_br0330 article-title: Canonical models in quantum scattering theory – year: 1989 ident: 10.1016/j.laa.2021.10.008_br0410 article-title: J-contractive matrix functions, reproducing kernel Hilbert spaces and interpolation – year: 1932 ident: 10.1016/j.laa.2021.10.008_br0640 – year: 2006 ident: 10.1016/j.laa.2021.10.008_br0440 – volume: vol. 26 year: 1989 ident: 10.1016/j.laa.2021.10.008_br0540 article-title: Scattering Theory – volume: vol. 200 year: 2010 ident: 10.1016/j.laa.2021.10.008_br0290 article-title: A state space approach to canonical factorization with applications – volume: 32 start-page: 603 year: 1985 ident: 10.1016/j.laa.2021.10.008_br0390 article-title: Minimal realizations of pseudo-positive and pseudo-bounded rational matrices publication-title: IEEE Trans. Circuits Syst. doi: 10.1109/TCS.1985.1085753 – volume: vol. 21 year: 2016 ident: 10.1016/j.laa.2021.10.008_br0460 article-title: The Theory of H(b) Spaces. Vol. 2 – year: 1986 ident: 10.1016/j.laa.2021.10.008_br0010 – start-page: 445 year: 1998 ident: 10.1016/j.laa.2021.10.008_br0650 article-title: Commuting operators and function theory on a Riemann surface – volume: 1 start-page: 107 issue: 2 year: 2003 ident: 10.1016/j.laa.2021.10.008_br0190 article-title: A family of Hilbert spaces which are not reproducing kernel Hilbert spaces publication-title: J. Anal. Appl. – volume: 373 year: 2020 ident: 10.1016/j.laa.2021.10.008_br0200 article-title: Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem publication-title: Adv. Math. doi: 10.1016/j.aim.2020.107315 – year: 1973 ident: 10.1016/j.laa.2021.10.008_br0570 article-title: Operator Colligations, Waves, Open Systems – volume: vol. 18 start-page: 89 year: 1986 ident: 10.1016/j.laa.2021.10.008_br0120 article-title: On applications of reproducing kernel spaces to the Schur algorithm and rational J-unitary factorization – volume: 61 start-page: 42 issue: 1 year: 2016 ident: 10.1016/j.laa.2021.10.008_br0180 article-title: A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions publication-title: Complex Var. Elliptic Equ. doi: 10.1080/17476933.2015.1053475 – volume: 8 start-page: 107 year: 1983 ident: 10.1016/j.laa.2021.10.008_br0270 article-title: A Beurling–Lax theorem for the Lie group U(m,n) which contains most classical interpolation theory publication-title: J. Oper. Theory – volume: 410 start-page: 2365 issue: 24–25 year: 2009 ident: 10.1016/j.laa.2021.10.008_br0370 article-title: On the similarity metric and the distance metric publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2009.02.023 – volume: 137/138 start-page: 413 year: 1990 ident: 10.1016/j.laa.2021.10.008_br0240 article-title: Structured invariant spaces of vector valued functions, sesquilinear forms, and a generalization of the Iohvidov laws publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(90)90137-2 – volume: 111 start-page: 1 year: 1993 ident: 10.1016/j.laa.2021.10.008_br0140 article-title: On a new class of structured reproducing kernel Hilbert spaces publication-title: J. Funct. Anal. doi: 10.1006/jfan.1993.1001 – volume: vol. 18 start-page: 301 year: 1986 ident: 10.1016/j.laa.2021.10.008_br0550 article-title: Triangular factorisation of structured Hermitian matrices – volume: 530 start-page: 15 year: 2017 ident: 10.1016/j.laa.2021.10.008_br0210 article-title: Beurling-Lax type theorems in the complex and quaternionic setting publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2017.04.037 – volume: 6 start-page: 250 year: 1983 ident: 10.1016/j.laa.2021.10.008_br0580 article-title: Cayley–Hamilton theorem, vector bundles and divisors of commuting operators publication-title: Integral Equ. Oper. Theory doi: 10.1007/BF01691898 – volume: 28 start-page: 77 issue: 2 year: 1983 ident: 10.1016/j.laa.2021.10.008_br0400 article-title: A class of invalid assertions concerning function Hilbert spaces publication-title: Bol. Soc. Mat. Mex. (2) – volume: 57 start-page: 173 issue: 2 year: 1977 ident: 10.1016/j.laa.2021.10.008_br0380 article-title: Simple C⁎-algebras generated by isometries publication-title: Commun. Math. Phys. doi: 10.1007/BF01625776 – year: 1994 ident: 10.1016/j.laa.2021.10.008_br0480 – volume: vol. 19 start-page: 275 year: 1986 ident: 10.1016/j.laa.2021.10.008_br0590 article-title: Commuting Nonselfadjoint Operators and Mappings of Vector Bundles on Algebraic Curves |
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| SubjectTerms | Analytic functions Backward-shift operator Beurling-Lax theorem Cuntz relations de Branges-Rovnyak spaces Linear algebra Mathematical analysis Multiplication Operators (mathematics) Rational functions Structure theorems Theorems |
| Title | Beurling-Lax type theorems and Cuntz relations |
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