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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 | : |
| Publisher | : |
| Total Pages | : 222 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
| 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 | : 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 | : Vladimir Müller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 444 |
| Release | : 2007-12-24 |
| Genre | : Mathematics |
| ISBN | : 3764382651 |
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. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.
| Author | : Abram Iezekiilovich Plesner |
| Publisher | : |
| Total Pages | : 256 |
| Release | : 1969 |
| Genre | : Mathematics |
| ISBN | : |
| 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 | : E. Brian Davies |
| Publisher | : Cambridge University Press |
| Total Pages | : 436 |
| Release | : 2007-04-26 |
| Genre | : Mathematics |
| ISBN | : 1139464337 |
This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.
| Author | : Aymen Ammar |
| Publisher | : CRC Press |
| Total Pages | : 284 |
| Release | : 2021-09-15 |
| Genre | : Mathematics |
| ISBN | : 1000293130 |
The concept of multivalued linear operators—or linear relations—is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators. The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations. The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.
| Author | : Israel Gohberg |
| Publisher | : Birkhäuser |
| Total Pages | : 428 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034879806 |
A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
