Bøker i Operator Theory: Advances and Applications-serien

This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam.

Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances.

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics.

This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research.

This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Boettcher's 60th birthday.

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics.

This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory.

This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor.The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event.They will be a valuable and inspiring source of information for graduate students and established researchers.

This volume is devoted to Joseph A. (Joe) Ball's contributions to operator theory and its applications and in celebration of his seventieth birthday.Joe Ball's career spans over four and a half decades, starting with his work on model theory and related topics for non-contractions and operators on multiply connected domains. Later on, more applied operator theory themes appeared in his work, involving factorization and interpolation for operator-valued functions, with extensive applications in system and control theory. He has worked on nonlinear control, time-varying systems and, more recently, on multidimensional systems and noncommutative H8-theory on the unit ball and polydisk, and more general domains, and these are only the main themes in his vast oeuvre.Fourteen research papers constitute the core of this volume, written by mathematicians who have collaborated with Joe or have been influenced by his vast mathematical work. A curriculum vitae, a publications list and a list of Joe Ball's PhD students are included in this volume, as well as personal reminiscences by colleagues and friends. Contributions by Yu. M. Arlinskii, S. Hassi, M. Augat, J. W. Helton, I. Klep, S. McCullough, S. Balasubramanian, U. Wijesooriya, N. Cohen, Q. Fang, S. Gorai, J. Sarkar, G. J. Groenewald, S. ter Horst, J. Jaftha, A. C. M. Ran, M.A. Kaashoek, F. van Schagen, A. Kheifets, Z. A. Lykova, N. J. Young, A. E. Ajibo, R. T. W. Martin, A. Ramanantoanina, M.-J. Y. Ou, H. J. Woerdeman, A. van der Schaft, A. Tannenbaum, T. T. Georgiou, J. O. Deasy and L. Norton.

This volume presents self-contained survey articles on modern research areas written by experts in their fields. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.

A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.

Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few.

The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics.

Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis.

The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.

This volume is dedicated to Leonid Lerer on the occasion of his seventieth birthday. The main part presents recent results in Lerer's research area of interest, which includes Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia type results, matrix polynomials, and related areas in operator and matrix theory.

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics.

Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis.

This collection presents various approaches to analytic problems that arise in the context of singular spaces. It contains articles offering introductions to various pseudodifferential calculi and discussions of relations between them, plus invited papers from mathematicians who have made significant contributions to this field

Written in honor of Victor Havin (1933-2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields.

In this monograph the natural evolution operators of autonomous first-order differential equations with exponential dichotomy on an arbitrary Banach space are studied in detail. This is the first book at graduate level on autonomous first-order differential equations with exponential dichotomy in a Banach space.

Table of Contents Preface . . . . . . . . . . . . . . . . . Kaashoek . Kaashoek . Kaashoek . Gohberg Opening Address . Woerdeman Personal Reminiscences . Mennicken On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices . Introduction . Conditions for the Separation of Spectral Components . Example . 9 References .

Uncertainty principles for time-frequency operators.- 1. Introduction.- 2. Sampling results for time-frequency transformations.- 3. Uncertainty principles for exact Gabor and wavelet frames.- References.- Distribution of zeros of matrix-valued continuous analogues of orthogonal polynomials.- 1. Preliminary results.- 1.1. Matrix-valued Krein functions of the first and second kinds.- 1.2. Partitioned integral operators.- 2. Orthogonal operator-valued polynomials.- 2.1. Stein equations for operators.- 2.2. Zeros of orthogonal polynomials.- 2.3. On Toeplitz matrices with operator entries.- 3. Zeros of mat rix-valued Krein functions.- 3.1 On Wiener-Hopf operators.- 3.2. Proof of the main theorem.- References.- The band extension of the real line as a limit of discrete band extensions, II. The entropy principle.- 0. Introduction.- I. Preliminaries.- II. Main results.- References.- Weakly positive matrix measures, generalized Toeplitz forms, and their applications to Hankel and Hilbert transform operators.- 1. Lifting properties of generalized Toeplitz forms and weakly positive matrix measures.- 2. The GBT and the theorems of Helson-Szeg¿ and Nehari.- 3. GNS construction, Wold decomposition and abstract lifting theorems.- 4. Multiparameter and n-conditional lifting theorems, the A-A-K theorem and applications in several variables.- References.- Reduction of the abstract four block problem to a Nehari problem.- 0. Introduction.- 1. Main theorems.- 2. Proofs of the main theorems.- References.- The state space method for integro-differential equations of Wiener-Hopf type with rational matrix symbols.- 1. Introduction and main theorems.- 2. Preliminaries on matrix pencils.- 3. Singular differential equations on the full-line.- 4. Singular differential equations on the half-line.- 5. Preliminaries on realizations.- 6. Proof of theorem 1.1.- 7. Proofs of theorems 1.2 and 1.3.- 8. An example.- References.- Symbols and asymptotic expansions.- 0. Introduction.- I. Smooth symbols on Rn.- II. Piecewise smooth symbols on T.- III. Piecewise smooth symbols on Rn.- IV. Symbols discontinuous across a hyperplane in Rn ¿Rn.- References.- Program of Workshop.