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| Author | : Francoise Chatelin |
| Publisher | : SIAM |
| Total Pages | : 482 |
| Release | : 2011-05-26 |
| Genre | : Mathematics |
| ISBN | : 0898719992 |
Originally published: New York: Academic Press, 1983.
| Author | : Wen-so Lo |
| Publisher | : |
| Total Pages | : 108 |
| Release | : 1972 |
| Genre | : Approximation theory |
| ISBN | : |
In this thesis we examine the approximation theory of the eigenvalue problem of bounded linear operators defined on a Banach space, and its applications to integral and differential equations. Special cases include the degenerate kernel method, projection method, collocation method, the Galerkin method, the method of moments, and the generalized Ritz method for solving integral or differential equations. Given a bounded linear operator, a sequence of bounded linear operator approximations is assumed to converge to it in the operator norm. We examine, among other things, the perturbation of the spectrum of the given operator; criteria for the existence and convergence of approximate eigenvectors and generalized eigenvectors; relations between the dimensions of the eigenmanifolds and generalized eigenmanifolds of the operator and those of the approximate operators.
| Author | : C. W. Groetsch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 134 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 3540399429 |
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
| Author | : Henry R. Dowson |
| Publisher | : |
| Total Pages | : 444 |
| Release | : 1978 |
| Genre | : Banach spaces |
| ISBN | : |
General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.
| Author | : David Edmunds |
| Publisher | : Oxford University Press |
| Total Pages | : |
| Release | : 2018-05-03 |
| Genre | : Mathematics |
| ISBN | : 0192540106 |
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 operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
| Author | : Aref Jeribi |
| Publisher | : Springer |
| Total Pages | : 608 |
| Release | : 2015-07-04 |
| Genre | : Science |
| ISBN | : 3319175661 |
Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.
| Author | : Mario Ahues |
| Publisher | : CRC Press |
| Total Pages | : 401 |
| Release | : 2001-02-26 |
| Genre | : Mathematics |
| ISBN | : 1420035827 |
Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for
| Author | : Roland Hagen |
| Publisher | : Birkhäuser |
| Total Pages | : 388 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034890672 |
The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.
| Author | : P.L. Butzer |
| Publisher | : Birkhäuser |
| Total Pages | : 461 |
| Release | : 2013-03-07 |
| Genre | : Mathematics |
| ISBN | : 3034893698 |
These Proceedings form a record of the lectures presented at the interna tional Conference on Functional Analysis and Approximation held at the Ober wolfach Mathematical Research Institute, August 9-16, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases.
| Author | : Seymour Goldberg |
| Publisher | : |
| Total Pages | : 312 |
| Release | : 1981 |
| Genre | : Mathematics |
| ISBN | : |
Basic Operator Theory provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, Basic Operator Theory begins with the geometry of Hilbert space and proceeds to the spectral theory for compact self-adjoint operators with a wide range of applications. Part of the volume is devoted to Banach spaces and operators acting on these spaces. Presented as a natural continuation of linear algebra, Basic Operator Theory provides a firm foundation in operator theory, an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
