Complex analysis and spectral theory : conference in celebration of Thomas Ransford's 60th birthday complex analysis and spectral theory, May 21-25, 2018, Laval University, Québec, Canada / H. Garth Dales, Dmitry Khavinson, Javad Mashreghi, editors.

Format:

Book

Author/Creator:

Dales, H. G. (Harold G.), 1944- editor.

Contributor:

Khavinson, Dmitry, 1956- editor.

Mashreghi, Javad, editor.

Ransford, Thomas, honoree.

Series:

Contemporary mathematics (American Mathematical Society). Centre de recherches mathématiques proceedings ; 0271-4132 743

Contemporary mathematics, 743 0271-4132

Centre de recherches mathématiques proceedings.

Language:

English

Subjects (All):

Functions of complex variables--Congresses.

Functions of complex variables.

Ransford, Thomas honoree.

Ransford, Thomas.

Physical Description:

1 online resource (296 pages).

Edition:

1st ed.

Place of Publication:

[Place of publication not identified] : American Mathematical Society, [2020]

Language Note:

English

Summary:

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.

Contents:

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

A holomorphic functional calculus for finite families of commuting semigroups

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

An integral Hankel operator on ¹( )

2. Definitions and pertinent background material

3. The embedding result

4. The corresponding measure

A panorama of positivity. II: Fixed dimension

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

Boundary values of holomorphic distributions in negative Lipschitz classes

2. The Problem

3. Results

4. Examples

5. Tools

6. Proofs of preliminary lemmas

7. Proofs of Theorems

8. Concluding remarks

Cyclicity in Dirichlet type spaces

1. Introduction and main result

2. Dirichlet space and duality

3. Cyclicity in \cD_{ }^{ }

Inner vectors for Toeplitz operators

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

Spectrum and local spectrum preservers of skew Lie products of matrices

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

Numerical range and compressions of the shift

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

On the asymptotics of -times integrated semigroups

2. Preliminaries and statement of the main theorem

3. Proofs

Powers of operators: convergence and decomposition

1. Powers of composition operators

2. Abstract decomposition

3. Decomposition of semigroups of operators

Back Cover.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-5453-X