تحلیل پیچیده و نظریه طیفی: کنفرانس در جشن تولد 60 سالگی توماس رنسفورد

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, Quebec, Canada. Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes). There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book. 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 P-pluripotential theory 1. Introduction 2. The global P-domination principle 3. Existence of strictly psh P-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 H1(D) 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 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_{α}^{p} 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 n-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 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 their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes). There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book. Contains the proceedings of the Conference on Complex Analysis and Spectral Theory, held in May 2018, at Laval University, Quebec. Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra.