This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan. I
Spectral theory for linear operators has become an important part of functional analysis and operator theory. This text seeks to define a spectrum for nonlinear operators that preserves the useful pro
This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introduct
These notes are based on six Fermi Lectures held at the Scuola Normale Superiore in Pisa in March and April 1981. The topics treated depend on basic concepts of classical mechanics, elementary geometr
This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory?and interpolation theory.?In particular, it?covers current
This concise text introduces techniques from quantum mechanics, especially scattering theory, to compute the effects of an external background on a quantum field in general, and on the properties of t
The first part of this monograph is dedicated to theoretical results. The first two chapters present the above mentioned survey on the joint spectral radius. Its minimum growth counterpart, the joint
This text offers background in function theory, Hardy functions, and probability as preparation for surveys of Gaussian processes, strings and spectral functions, and strings and spaces of integral fu
This volume brings together lectures from an instructional meeting on spectral theory and geometry held under the auspices of the International Centre for Mathematical Sciences in Edinburgh. The contributions here come from world experts and many are much expanded versions of the lectures they gave. Together they survey the core material and go beyond to reach deeper results. For graduate students and experts alike, this book will be a highly useful resource.
This major, two-volume work is devoted to the methods of the spectral theory of operators and the important role they play in infinite-dimensional analysis and its applications. Central to this stu
The present volume contains the Proceedings of the International Conference Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. The book presents survey articles
An advanced monograph on a central topic in the theory of differential equations, Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators. While the study of the heat equation is a classical subject, this book analyses the improvements in our quantitative understanding of heat kernels. The author considers variable coefficient operators on regions in Euclidean space and Laplace-Beltrami operators on complete Riemannian manifolds. He also includes results pertaining to the heat kernels of Schrödinger operators; such results will be of particular interest to mathematical physicists, and relevant too to those concerned with properties of Brownian motion and other diffusion processes.
This book is an introduction to the theory of partial differential operators. It assumes that the reader has a knowledge of introductory functional analysis, up to the spectral theorem for bounded linear operators on Banach spaces. However, it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator. A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second-order elliptic differential operators, from those with discrete spectrum to Schrödinger operators acting on L2(RN). The book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on the subjec
Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.
This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear opera
