Bücher der Reihe Operator Theory: Advances and Applications

This monograph presents the solution of the classical moment problem, the construction of Jacobi matrices and corresponding polynomials. The cases of strongly,trigonometric, complex and real two-dimensional moment problems are discussed, and the Jacobi-type matrices corresponding to the trigonometric moment problem are shown. The Berezansky theory of the expansion in generalized eigenvectors for corresponding set of commuting operators plays the key role in the proof of results.The book is recommended for researchers in fields of functional analysis, operator theory, mathematical physics, and engineers who deal with problems of coupled pendulums.

This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.The book has two central themes: the trace formula and inverse problems.The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book.To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions.The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.

This monograph presents necessary and sufficient conditions for completeness of the linear span of eigenvectors and generalized eigenvectors of operators that admit a characteristic matrix function in a Banach space setting. Classical conditions for completeness based on the theory of entire functions are further developed for this specific class of operators. The classes of bounded operators that are investigated include trace class and Hilbert-Schmidt operators, finite rank perturbations of Volterra operators, infinite Leslie operators, discrete semi-separable operators, integral operators with semi-separable kernels, and period maps corresponding to delay differential equations. The classes of unbounded operators that are investigated appear in a natural way in the study of infinite dimensional dynamical systems such as mixed type functional differential equations, age-dependent population dynamics, and in the analysis of the Markov semigroup connected to the recently introduced zig-zag process.

This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians.Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. Garcia, L.G. Garza, F. Gesztesy, D. Gomez-Ullate, Y. Grandati, F.A. Grunbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellan, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velazquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.

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

The topics range from C*-algebras and Banach *-algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces.

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings.

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings.

This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017.

This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology.

The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Brown, D. Fillman, D. Gesztesy, D. Martinez-Finkelshtein, D. Milson, D. Novello, D.

These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations.

The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.

Victor comes to Rehovot.- My Teacher Viktor Emmanuilovich Katsnelson.- Some impressions of Viktor Emmanuilovich Katsnelson.- The good fortune of maintaining a long-lasting close friendship and scientic collaboration with V. E. Katsnelson.- A piece of Victor Katsnelsons mathematical biography.- Interpolation by contractive multipliers between Fock spaces.- Regular extensions and defect functions of contractive measurable operator-valued functions.- Free-homomorphic relations induced by certain free semicircular families.- Self-adjoint extensions of a symmetric linear relation with nite defect: compressions and Straus subspaces.- On conditions for complete indeterminacy of the matricial Hamburger moment problem.- On a Blaschke-type condition for subharmonic function with two sets of singularities on the boundary.- Exponential Taylor domination.- A closer look at the solution of the truncated matricial moment problem.- On a class of sectorial relations and the associated closed forms.- Spectral decompositions of selfadjoint relations in Pontryagin spaces and factorizations of generalized Nevanlinna functions.- Martin functions of Fuchsian groups and character automorphic subspaces of the Hardy space in the upper half-plane.

Commutative Banach algebras generated by Toeplitz operators on the unit ball.- Toeplitz operators on Fock space: revisiting some old problems.- Laplace-Beltrami equation on surfaces with the Lipschitz boundary.- Reproducing kernels and distinguished metrics.- Fock-Carleson type measures and horizontal Toeplitz operators.- Asymptotics of all eigenvalues of large non self-adjoint Toeplitz Matrices.- A semi-classical limit with applications to Toeplitz algebras.- Solving twofold Ellis-Gohberg inverse problems.- A C*-algebra of nonlocal convolution type operators.- The Maslov index and the spectrum of differential operators.- Toeplitz operators on the unit sphere.- Diagonalization of translation-invariant operators in reproducing kernel Hilbert spaces.- Toeplitz operators and representation theory.- On "all but m" families of projections.- Szego theorems for singular Toeplitz operators in the Bargmann space.- Toeplitz operators with radial symbols.- Schrodinger operators with singular potentials supported by unbounded hypersurfaces.- Toeplitz Operators on the Poly-Bergman Spaces of the Upper Half-Plane.- Polyanalytic Spaces.- Algebras Generated by Toeplitz Operator on the Siegel Domain.- On the essential norms of Toeplitz operators.- Making the case for pseudodifferential arithmetic.- Reproducing kernels and Toeplitz operators on Kepler varieties.- Compact quantum surfaces from the Toeplitz algebra.- Sarason''s Toeplitz product problem.

This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.

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

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 monograph discusses covariant Schroedinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schroedinger operators has mainly focused on scalar Schroedinger operators on Euclidean spaces so far.

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.

The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra.

This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications.

Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M.

This text establishes a theory for general linear parabolic partial differential equations that covers equations with inhomogeneous symbol structure as well as mixed-order systems.