Bøger i Operator Theory: Advances and Applications serien

Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics.

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.

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

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.

This book presents novel results by participants of the conference "Control theory of infinite-dimensional systems" that took place in January 2018 at the FernUniversitat in Hagen.

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 defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis.

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.