Bücher der Reihe Operator Theory: Advances and Applications

Contains some of the invited lectures presented at the International Conference Analysis, PDEs and Applications, held in Rome in July 2008, and dedicated to Vladimir G Maz'ya on the occasion of his 70th birthday. This title present surveys as well as fresh results in the areas in which Maz'ya gave seminal contributions.

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements.

Constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics that was held in Prague, Czech Republic in June, 1998. This title addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schrodinger and Pauli operators.

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications.

This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications.

This book consists of translations into English of several pioneering papers in the areas of discrete and continuous convolution operators and on the theory of singular integral operators published originally in Russian.

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors.

This book systematically studies the asymptotic behavior, in particular "stability" in some sense, for discrete and continuous linear dynamical systems on Banach spaces. Of special concern is convergence to an equilibrium regarding various topologies.

Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators.

This book presents recent results in the following areas: spectral analysis of one-dimensional Schroedinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators.

Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators.

Consists of twenty peer-reviewed papers from the special session on pseudo differential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples' Friendship University of Russia in Moscow on August 22a'27, 2011.

Boundary value problems for elliptic differential-difference equations have some astonishing properties. The book is addresssed to graduate students and researchers in partial differential equations and functional differential equations.

The conference Operator Theory, Analysis and Mathematical Physics - OTAMP is a regular biennial event devoted to mathematical problems on the border between analysis and mathematical physics.

This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011.

A collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators) close to Professor Rabinovich's research interests.

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

The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences.

The monograph is devoted to the study of functional equations with the transformed argument on the real line and on the unit circle.

Contains articles based on lectures given at the International Conference on Pseudo-differential Operators and Related Topics at Vaxjo University in Sweden from June 22 to June 25, 2005. Sixteen refereed articles cover a spectrum of topics such as partial differential equations, Wigner transforms, mathematical physics, and more.

This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator.

This unique book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space over the unit disk.

This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems.

This trail-blazing treatment of a new and emerging topic sets out the authors' own research into differing interpretations of the semi-boundedness of partial differential operators. It examines function spaces that include the Hilbert and Banach varieties.

The conference is now over and enough time has passed for us to realize that the concensus of opinion of the participants is that it was indeed a successful and fruitful conference. This conference showed just how wide spread are the ideas of Otto Toeplitz, and how strong an influence his work has. The majority of participants contributed papers for this volume, which will help to bring to this interesting conference a wider audience. About the background and organization of the conference, the reader can learn from the opening address, which is included in place of an introduction. In my opinion this volume would be of interest to a wide public; experts in pure and applied mathematics as well as persons interested in the history of mathematics. The papers are divided into two sections. The first section is given to research papers, and the second to memorial papers. We are indebted to Professor G. K8the who allowed us to publish in the section of memorial papers the translation into English of his talk, given at a Colloquium in honour of Otto Toeplitz in Bonn. During the preparation of this volume great assistance was extended to us by Dr. Uri Toeplitz and Mrs. G. Riesel to whom I would like to express my sincere gratitude. I would like to take this opportunity to thank all persons and organizations who helped to make this conference such a success, and also Birkhauser Verlag for publishing this volume of the Proceedings.

The development of many important directions of mathematics and physics owes a major debt to the concepts and methods which evolved during the investigation of such simple objects as the Sturm-Liouville equation 2 2 y" + q(x)y = zy and the allied Sturm-Liouville operator L = - d /dx + q(x) (lately Land q(x) are often termed the one-dimensional Schrödinger operator and the potential). These provided a constant source of new ideas and problems in the spectral theory of operators and kindred areas of analysis. This sourse goes back to the first studies of D. Bernoulli and L. Euler on the solution of the equation describing the vibrations of astring, and still remains productive after more than two hundred years. This is confirmed by the recent discovery, made by C. Gardner, J. Green, M. Kruskal, and R. Miura [6J, of an unexpected connection between the spectral theory of Sturm-Liouville operators and certain nonlinear partial differential evolution equations. The methods used (and often invented) during the study of the Sturm-Liouville equation have been constantly enriched. In the 40's a new investigation tool joined the arsenal - that of transformation operators.

Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006.

This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly involving developed extension theory in triplets of rigged Hilbert spaces and unbounded operators as state-space operators of linear systems. The connections of the realization theory to systems with accretive, sectorial, and contractive state-space operators as well as to the Phillips-Kato sectorial extension problem, the Krein-von Neumann and Friedrichs extremal extensions are provided. Among other results the book contains applications to the inverse problems for linear systems with non-self-adjoint Schrodinger operators, Jacobi matrices, and to the Nevanlinna-Pick system interpolation.

In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of operator semigroups. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems.