Complex Analysis and Spectral Theory
This volume contains the proceedings of the Conference on Complex Analysis and Spectral Theory, in celebration of Thomas Ransford's 60th birthday, held from May 21-25, 2018, at Laval University, Québec, Canada. Spectral theory is the branch of mathematics devoted to the study of matrices and th...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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American Mathematical Society
2020
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| Vydání: | 1 |
| Edice: | Contemporary Mathematics. Centre De Recherches Mathématiques Proceedings |
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| ISBN: | 9781470446925, 1470446928 |
| On-line přístup: | Získat plný text |
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- 2.1. From metric geometry to matrix positivity -- 2.2. Entrywise functions preserving positivity in all dimensions -- 2.3. The Horn-Loewner theorem and its variants -- 2.4. Preservers of positive Hankel matrices -- 3. Entrywise polynomials preserving positivity in fixed dimension -- 3.1. Characterizations of sign patterns -- 3.2. Schur polynomials -- the sharp threshold bound for a single matrix -- 3.3. The threshold for all rank-one matrices: a Schur positivity result -- 3.4. Real powers -- the threshold works for all matrices -- 3.5. Power series preservers and beyond -- unbounded domains -- 3.6. Digression: Schur polynomials from smooth functions, and new symmetric function identities -- 3.7. Further applications: linear matrix inequalities, Rayleigh quotients, and the cube problem -- 3.8. Entrywise preservers of totally non-negative Hankel matrices -- 4. Power functions -- 4.1. Sparsity constraints -- 4.2. Rank constraints and other Loewner properties -- 5. Motivation from statistics -- 5.1. Thresholding with respect to a graph -- 5.2. Hard and soft thresholding -- 5.3. Rank and sparsity constraints -- Table of contents from Part I of the survey -- References -- Boundary values of holomorphic distributions in negative Lipschitz classes -- 1. Introduction -- 2. The Problem -- 3. Results -- 4. Examples -- 5. Tools -- 6. Proofs of preliminary lemmas -- 7. Proofs of Theorems -- 8. Concluding remarks -- References -- Cyclicity in Dirichlet type spaces -- 1. Introduction and main result -- 2. Dirichlet space and duality -- 3. Cyclicity in \cD_{ }^{ } -- References -- Inner vectors for Toeplitz operators -- 1. Introduction -- 2. Basic definitions and facts -- 3. Inner vectors via the Wold decomposition -- 4. Inner vectors via the operator-valued Poisson kernel -- 5. Inner vectors via Clark measures -- 6. Inner vectors in model spaces -- References
- Jack and Julia -- 1. Introduction and statement of the main result -- 2. Proof of our main result -- 3. Two special cases -- References -- Spectrum and local spectrum preservers of skew Lie products of matrices -- 1. Introduction -- 2. Main results -- 3. Spectra and skew Lie product -- 4. Local spectra and skew Lie product -- 5. A local spectral identity principal -- 6. Useful dense and spanning subsets of \mn -- 7. Proofs of the main results -- References -- Numerical range and compressions of the shift -- 1. Introduction -- 2. Numerical Ranges and Envelopes -- 3. The numerical range of a compressed shift operator (single variable) -- 4. Extensions: General inner functions and other defect indices -- 5. Compressed shifts on the bidisk -- 6. Open Questions -- References -- On the asymptotics of -times integrated semigroups -- 1. Introduction -- 2. Preliminaries and statement of the main theorem -- 3. Proofs -- References -- Powers of operators: convergence and decomposition -- 1. Powers of composition operators -- 2. Abstract decomposition -- 3. Decomposition of semigroups of operators -- References -- Back Cover
- Cover -- Title page -- Contents -- Preface -- List of Invited Speakers -- Additive maps preserving matrices of inner local spectral radius zero at some fixed vector -- 1. Introduction and statement of results -- 2. Preliminary results -- 3. Proof of the main result -- References -- A global domination principle for -pluripotential theory -- 1. Introduction -- 2. The global -domination principle -- 3. Existence of strictly psh -potential -- 4. The product property -- References -- A holomorphic functional calculus for finite families of commuting semigroups -- 1. Introduction -- 2. Quasimultipliers on weakly cancellative commutative Banach algebras with dense principal ideals -- 3. Normalization of a commutative Banach algebra with respect to a strongly continuous semigroup of multipliers -- 4. Normalization of a commutative Banach algebra with respect to a holomorphic semigroup of multipliers -- 5. Generator of a strongly continuous semigroup of multipliers and Arveson spectrum -- 6. The resolvent -- 7. The generator of a holomorphic semigroup and its resolvent -- 8. Multivariable functional calculus associated to linear functionals -- 9. Multivariable functional calculus associated to holomorphic functions of several complex variables -- 10. Appendix 1: Fourier-Borel and Cauchy transforms -- 11. Appendix 2: An algebra of fast-decreasing holomorphic functions on products of sectors and half-lines and its dual -- 12. Appendix 3: Holomorphic functions on admissible open sets -- References -- An integral Hankel operator on ¹( ) -- 1. Introduction -- 2. Definitions and pertinent background material -- 3. The embedding result -- 4. The corresponding measure -- References -- A panorama of positivity. II: Fixed dimension -- 1. Introduction -- 2. A selection of classical results on entrywise positivity preservers