Spectral Theory Of Linear Operators
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Spectral Approximation Of Linear Operators
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Author : Françoise Chaitin-Chatelin
language : en
Publisher:
Release Date : 1983
Spectral Approximation Of Linear Operators written by Françoise Chaitin-Chatelin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
The goal of this book is to be comprehensive, running the gamut from practical numerical results to a unifying framework of functional analysis, while simultaneously preserving the energy and excitement of presenting fresh research results. Its contents cover recent results, which either are scattered through the literature or appear here for the first time, as well as providing a nontraditional presentation of standard material.
Spectral Theory Of Hyponormal Operators
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Author : Xia
language : en
Publisher: Birkhäuser
Release Date : 2013-11-22
Spectral Theory Of Hyponormal Operators written by Xia and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Social Science categories.
Spectral analysis of linear operators has always been one of the more active and important fields of operator theory, and of extensive interest to many operator theorists. Its devel opments usually are closely related to certain important problems in contemporary mathematics and physics. In the last 20 years, many new theories and interesting results have been discovered. Now, in this direction, the fields are perhaps wider and deeper than ever. This book is devoted to the study of hyponormal and semi-hyponormal operators. The main results we shall present are those of the author and his collaborators and colleagues, as well as some concerning related topics. To some extent, hyponormal and semi-hyponormal opera tors are "close" to normal ones. Although those two classes of operators contain normal operators as a subclass, what we are interested in are, naturally, nonnormal operators in those classes. With the well-studied normal operators in hand, we cer tainly wish to know the properties of hyponormal and semi-hypo normal operators which resemble those of normal operators. But more important than that, the investigations should be concen trated on the phenomena which only occur in the nonnormal cases.
Spectral Theory Of Linear Operators
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Author : Henry R. Dowson
language : en
Publisher:
Release Date : 1978
Spectral Theory Of Linear Operators written by Henry R. Dowson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.
Perturbation Theory For Linear Operators
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Author : Tosio Kato
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Perturbation Theory For Linear Operators written by Tosio Kato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Nonlinear Spectral Theory
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Author : Jürgen Appell
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Nonlinear Spectral Theory written by Jürgen Appell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
Linear Operators In Hilbert Spaces
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Author : Joachim Weidmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Operators In Hilbert Spaces written by Joachim Weidmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential operators.
Introduction To Spectral Theory
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Author : P.D. Hislop
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Spectral Theory written by P.D. Hislop and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras
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Author : Vladimir Müller
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras written by Vladimir Müller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Spectral theory is an important part of functional analysis.It has numerous appli cations in many parts of mathematics and physics including matrix theory, func tion theory, complex analysis, differential and integral equations, control theory and quantum physics. In recent years, spectral theory has witnessed an explosive development. There are many types of spectra, both for one or several commuting operators, with important applications, for example the approximate point spectrum, Taylor spectrum, local spectrum, essential spectrum, etc. The present monograph is an attempt to organize the available material most of which exists only in the form of research papers scattered throughout the literature. The aim is to present a survey of results concerning various types of spectra in a unified, axiomatic way. The central unifying notion is that of a regularity, which in a Banach algebra is a subset of elements that are considered to be "nice". A regularity R in a Banach algebra A defines the corresponding spectrum aR(a) = {A E C : a - ,\ rJ. R} in the same way as the ordinary spectrum is defined by means of invertible elements, a(a) = {A E C : a - ,\ rJ. Inv(A)}. Axioms of a regularity are chosen in such a way that there are many natural interesting classes satisfying them. At the same time they are strong enough for non-trivial consequences, for example the spectral mapping theorem.
Spectral Theory Of Linear Operators
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Author : Abram Iezekiilovich Plesner
language : en
Publisher:
Release Date : 1969
Spectral Theory Of Linear Operators written by Abram Iezekiilovich Plesner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Linear Operators
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Author : Richard G. Cooke
language : en
Publisher:
Release Date : 1953
Linear Operators written by Richard G. Cooke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Algebra, Universal categories.