Search Results - Orthogonal functions and polynomials, general theory of trigonometric harmonic analysis

On the orthonormal Franklin system

Authors: Nemeth, Jozsef

Source: Publicationes Mathematicae Debrecen. 19:181-185

Subject Terms: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Best approximation, Chebyshev systems, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Convergence and absolute convergence of Fourier and trigonometric series, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences

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Access URL: https://zbmath.org/3419698

Orthogonal Rational Functions and Frequency Analysis: Orthogonal rational functions and frequency analysis

Authors: Haakon Waadeland

Source: Acta Applicandae Mathematica. 61:367-377

Subject Terms: orthogonal rational function, 0101 mathematics, trigonometric signal scheduling, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Application of orthogonal and other special functions, 01 natural sciences

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Access URL: https://zbmath.org/1546754
https://doi.org/10.1023/a:1006417408359
https://link.springer.com/article/10.1023/A%3A1006417408359
https://link.springer.com/content/pdf/10.1023/A:1006417408359.pdf

Fast conversion algorithms for orthogonal polynomials

Authors: Alin Bostan Éric Schost Bruno Salvy

Source: Linear Algebra and its Applications. 432:249-258

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, Basis conversion, fast algorithms, Orthogonal polynomials, Analysis of algorithms and problem complexity, Numerical methods for trigonometric approximation and interpolation, conversion algorithms, 0102 computer and information sciences, transposed algorithms, Symbolic Computation (cs.SC), Transposed algorithms, 01 natural sciences, Fast algorithms, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Complexity and performance of numerical algorithms, Discrete Mathematics and Combinatorics, Analysis of algorithms, Numerical approximation and evaluation of special functions, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, basis conversion, orthogonal polynomials, Numerical Analysis, Algebra and Number Theory, Computation of special functions and constants, construction of tables, Geometry and Topology, complexity

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Access URL: http://arxiv.org/abs/0804.2373
https://zbmath.org/5650034
https://doi.org/10.1016/j.laa.2009.08.002
https://arxiv.org/abs/0804.2373
https://arxiv.org/pdf/0804.2373.pdf
https://hal.archives-ouvertes.fr/inria-00273508
https://core.ac.uk/display/81116146
http://www.csd.uwo.ca/~eschost/publications/BoSaSc08b-r1.pdf
https://www.sciencedirect.com/science/article/pii/S002437950900408X

Determinants with orthogonal polynomial entries

Authors: Ismail, Mourad E.H.

Source: Journal of Computational and Applied Mathematics. 178:255-266

Subject Terms: Al-Salam-Chihara, Moments, Trigonometric moment problems in one variable harmonic analysis, polynomials, Applied Mathematics, Turin determinants, Turán determinants, Determinants, permanents, traces, other special matrix functions, JACOBI POLYNOMIALS, 01 natural sciences, REPRESENTATIONS, q-ultraspherical polynomials, Computational Mathematics, Turan determinants, Al-Salam-Chihara polynomials, \(q\)-ultraspherical polynomials, Applied, FORMULAS, moments, 0101 mathematics, INEQUALITY, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematics, Hankel determinants

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Access URL: https://zbmath.org/2157673
https://doi.org/10.1016/j.cam.2004.01.042
https://ui.adsabs.harvard.edu/abs/2005JCoAM.178..255I/abstract
https://www.sciencedirect.com/science/article/pii/S0377042704003784
https://www.sciencedirect.com/science/article/abs/pii/S0377042704003784

Boundary Asymptotics for Orthogonal Rational Functions on the Unit Circle: Boundary asymptotics for orthogonal rational functions on the unit circle

Authors: Bultheel, Adhemar Van gucht, Patrick

Source: Acta Applicandae Mathematica. 61:333-349

Subject Terms: Science & Technology, General Mathematics, Trigonometric approximation, Mathematics, Applied, orthogonal rational functions, 16. Peace & justice, 6. Clean water, 0101 Pure Mathematics, asymptotics, 0102 Applied Mathematics, Physical Sciences, 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics, 4904 Pure mathematics, 4901 Applied mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematics

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Access URL: https://lirias.kuleuven.be/bitstream/123456789/123900/1/icra99.pdf
https://zbmath.org/1546752
https://doi.org/10.1023/a:1006409205633
https://link.springer.com/article/10.1023/A%3A1006409205633
https://link.springer.com/content/pdf/10.1023/A:1006409205633.pdf

Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces II: numerical stability: Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces. II: numerical stability

Authors: Roberto Barrio Sergio Serrano

Source: Journal of Computational and Applied Mathematics. 181:299-320

Subject Terms: Rounding errors, Roundoff error, Applied Mathematics, Recurrence relations, Numerical methods for trigonometric approximation and interpolation, algorithms, 01 natural sciences, Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Sobolev orthogonal polynomials, Computational Mathematics, Computation of special functions and constants, construction of tables, numerical stability, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

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Access URL: https://www.sciencedirect.com/science/article/pii/S0377042704005862
https://ui.adsabs.harvard.edu/abs/2005JCoAM.181..299B/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0377042704005862
https://core.ac.uk/display/82361477

On the Convergence of Fourier Series with Orthogonal Polynomials inside and on the Closure of a Region: On convergence of the Fourier series with orthogonal polynomials inside and on the closure of a region

Authors: Abdullaev F.G. Küçükaslan M. Çukurova Üniversitesi

Contributors: Abdullaev F.G. Küçükaslan M. Çukurova Üniversitesi

Source: Ukrainian Mathematical Journal. 54:1567-1582

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Convergence and absolute convergence of Fourier and trigonometric series, Miscellaneous topics of analysis in the complex plane, ????????????, 16. Peace & justice, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Fourier series, orthogonal polynomials, rate of convergence

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Access URL: https://zbmath.org/1961288
https://doi.org/10.1023/a:1023705500910
https://link.springer.com/article/10.1023%2FA%3A1023705500910
http://dspace.nbuv.gov.ua/handle/123456789/164298

Modification of a method using Szegö polynomials in frequency analysis: the V-process: Modification of a method using Szegő polynomials in frequency analysis: The \(V\)-process

Authors: Vigdis Brevik Petersen

Source: Journal of Computational and Applied Mathematics. 133:535-544

Subject Terms: Signal theory (characterization, reconstruction, filtering, etc.), Szegő polynomials, trigonometric signal, Applied Mathematics, frequency analysis, Szegö polynomial, modifications, Toeplitz determinant, Toeplitz determinants, Application of orthogonal and other special functions, 01 natural sciences, Zeros, Computational Mathematics, moments, Frequency analysis, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

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Access URL: https://zbmath.org/1659299
https://doi.org/10.1016/s0377-0427(00)00674-9
https://www.sciencedirect.com/science/article/abs/pii/S0377042700006749
https://ui.adsabs.harvard.edu/abs/2001JCoAM.133..535P/abstract
https://www.sciencedirect.com/science/article/pii/S0377042700006749
https://dialnet.unirioja.es/servlet/articulo?codigo=725318

A case of Toeplitz determinants and theta functions in frequency analysis

Authors: Vigdis Brevik Petersen Haakon Waadeland

Source: Journal of Computational and Applied Mathematics. 139:239-251

Subject Terms: trigonometric signal, Applied Mathematics, frequency analysis, Toeplitz determinant, Application of orthogonal and other special functions, 01 natural sciences, Computational Mathematics, Carathéodory function, theta function, Theta function, Frequency analysis, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials

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Access URL: https://zbmath.org/1743072
https://doi.org/10.1016/s0377-0427(01)00422-8
http://ui.adsabs.harvard.edu/abs/2002JCoAM.139..239P/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0377042701004228#!
https://www.sciencedirect.com/science/article/pii/S0377042701004228

Modified Moments and Matrix Orthogonal Polynomials: Modified moments and matrix orthogonal polynomials

Authors: E. Bourreau

Source: Acta Applicandae Mathematica. 61:53-64

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), modified moments, Computation of special functions and constants, construction of tables, biorthogonality, numerial examples, Numerical methods for trigonometric approximation and interpolation, modified Chebyshev algorithm, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1023/A%3A1006419830281

Quadrature formula and zeros of para-orthogonal polynomials on the unit circle

Authors: Leonid Golinski

Source: Acta Mathematica Hungarica. 96:169-186

Subject Terms: measures on the unit circle, para-orthogonal polynomials, trigonometric moment problem, Szegő quadrature problem, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences

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Access URL: https://zbmath.org/1960298
https://doi.org/10.1023/a:1019765002077
https://link.springer.com/article/10.1023/A:1019765002077

Asymptotics for zeros of Szegő polynomials associated with trigonometric polynomial signals

Authors: Edward B. Saff K. Pan

Source: Journal of Approximation Theory. 71:239-251

Subject Terms: Mathematics(all), Numerical Analysis, Applied Mathematics, Trigonometric polynomials, inequalities, extremal problems, trigonometric polynomials, Wiener-Levinson digital filter, Szegö polynomials, frequencies, Application of orthogonal and other special functions, periodic discrete time signal, 01 natural sciences, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Analysis

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Access URL: https://zbmath.org/86110
https://doi.org/10.1016/0021-9045(92)90118-8
https://core.ac.uk/display/82283500
https://www.sciencedirect.com/science/article/pii/0021904592901188
https://www.sciencedirect.com/science/article/abs/pii/0021904592901188

The stable computation of formal orthogonal polynomials

Authors: Bernhard Beckermann

Source: Numerical Algorithms. 11:1-23

Subject Terms: Computation of special functions and constants, construction of tables, Cabay-Meleshko algorithm, Numerical methods for trigonometric approximation and interpolation, pairs of basis polynomials, stability parameters, 0101 mathematics, formal orthogonal polynomials, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences, error analysis, condition number, Hankel matrix of moments

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Access URL: https://dblp.uni-trier.de/db/journals/na/na11.html#Beckermann96
https://ui.adsabs.harvard.edu/abs/1996NuAlg..11....1B/abstract
https://link.springer.com/article/10.1007/BF02142485

Szegő polynomials applied to frequency analysis

Authors: William B. Jones Olav Njåstad W. J. Thron et al.

Source: Journal of Computational and Applied Mathematics. 46:217-228

Subject Terms: Wiener-Levinson filters, convergence, Applied Mathematics, frequency analysis, Numerical methods for trigonometric approximation and interpolation, Szegö polynomials, Wiener- Levinson method, Application of orthogonal and other special functions, 01 natural sciences, Computational Mathematics, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Padé approximants, Frequency analysis, discrete signals, 0101 mathematics, orthogonal polynomials, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Padé approximation, Levinson's algorithm

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Access URL: https://zbmath.org/219122
https://doi.org/10.1016/0377-0427(93)90297-o
https://www.sciencedirect.com/science/article/pii/037704279390297O
https://www.sciencedirect.com/science/article/abs/pii/037704279390297O
https://www.sciencedirect.com/science/article/pii/037704279390297O#!

Asymptotic properties of zeros of orthogonal rational functions

Authors: Haakon Waadeland Olav Njåstad

Source: Journal of Computational and Applied Mathematics. 77:255-275

Subject Terms: Computational Mathematics, zeros of orthogonal rational functions, unknown frequencies, trigonometric signal, Applied Mathematics, Zeros of orthogonal rational functions, frequency analysis, Frequency analysis, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Application of orthogonal and other special functions, 01 natural sciences

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Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0377042796001306
https://www.sciencedirect.com/science/article/pii/S0377042796001306

A survey of certain results on strong approximation by orthogonal series

Authors: László Leindler

Source: Open Mathematics, Vol 2, Iss 3, Pp 448-477 (2004)

Subject Terms: 40c15, 42c15, Trigonometric approximation, fourier series, 41-02, Research exposition (monographs, survey articles) pertaining to approximations and expansions, 01 natural sciences, Trong approximation, strong approximation, summability methods, QA1-939, 0101 mathematics, orthogonal series, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 42a24, 40c05, 42c05, 40f05, Rate of convergence, degree of approximation, Absolute and strong summability, General harmonic expansions, frames, Fourier series, Matrix methods for summability, Summability and absolute summability of Fourier and trigonometric series, 42a10, Function-theoretic methods (including power series methods and semicontinuous methods) for summability, 41a25, Mathematics

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Access URL: https://zbmath.org/2143680
https://doi.org/10.2478/bf02475239
https://doaj.org/article/da1c1fc877dc40b098e5d0549ef0ceb9
https://link.springer.com/article/10.2478%2FBF02475239
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.doi-10_2478_BF02475239
https://eudml.org/doc/268924
https://www.degruyter.com/view/j/math.2004.2.issue-3/BF02475239/bf02475239.xml

On the solution of inverse problems and trigonometric forms for the Geronimus polynomials. Application to the theory of iterative methods

Authors: V. I. Lebedev

Source: Russian Journal of Numerical Analysis and Mathematical Modelling. 15

Subject Terms: Iterative numerical methods for linear systems, inverse problems, three-term recurrence relations, 01 natural sciences, linear operator equations, Computation of special functions and constants, construction of tables, iterative method, Numerical solutions to equations with linear operators, Geronimus polynomials, iterative methods, Spectrum, resolvent, Numerical methods for functional equations, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

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Access URL: https://zbmath.org/1436034
https://doi.org/10.1515/rnam.2000.15.1.73
https://www.degruyter.com/view/j/rnam.2000.15.issue-1/rnam.2000.15.1.73/rnam.2000.15.1.73.xml

Conservative Means of Orthogonal Series and the Spaces $$L^p [0;1] $$ , $$p \in (1;\infty ) $$: Conservative means of orthogonal series and the spaces \(L^ p[0;1]\), \(p\in(1;\infty)\)

Authors: I. N. Brui

Source: Mathematical Notes. 71:166-176

Subject Terms: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), summation method, Summability and absolute summability of Fourier and trigonometric series, multiplier, 0101 mathematics, orthogonal series, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Fourier series, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1023/A%3A1013951012900
https://link.springer.com/content/pdf/10.1023/A:1013951012900.pdf

A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩>2l: A singular Riesz product in the Nevai class and inner functions with the Schur parameters in \(\cap_{p>2}I^p\)

Authors: Sergei Khrushchev

Source: Journal of Approximation Theory. 108:249-255

Subject Terms: Mathematics(all), Numerical Analysis, Applied Mathematics, Riesz product, Other special orthogonal polynomials and functions, Blaschke products, etc, Lacunary series of trigonometric and other functions, Riesz products, 01 natural sciences, orthonormal polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Geronimus parameters, Blaschke product, 0101 mathematics, Nevai class, orthogonal polynomials, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Schur parameters, Analysis

File Description: application/xml

Access URL: https://zbmath.org/1594688
https://doi.org/10.1006/jath.2000.3501
https://dblp.uni-trier.de/db/journals/jat/jat108.html#Khrushchev01a
https://www.sciencedirect.com/science/article/pii/S0021904500935019
https://core.ac.uk/display/82008674

Géza Freud, orthogonal polynomials and Christoffel functions. A case study

Authors: Paul Neval

Source: Journal of Approximation Theory. 48:3-167

Subject Terms: Mathematics(all), Numerical Analysis, Tauberian theorems, Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces, Applied Mathematics, Convergence and absolute convergence of Fourier and trigonometric series, Absolute and strong summability, convergence of orthogonal Fourier series, Freud-weights, 01 natural sciences, strong Cesáro summability, Cesàro, Euler, Nörlund and Hausdorff methods, Christoffel functions, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Analysis

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Access URL: https://www.sciencedirect.com/science/article/pii/002190458690016X
https://www.sciencedirect.com/science/article/abs/pii/002190458690016X