Spectral Theory of Multivalued Linear Operators
Title | Spectral Theory of Multivalued Linear Operators PDF eBook |
Author | Aymen Ammar |
Publisher | CRC Press |
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.
Spectral Theory of Multivalued Linear Operators
Title | Spectral Theory of Multivalued Linear Operators PDF eBook |
Author | Aymen Ammar |
Publisher | CRC Press |
Pages | 314 |
Release | 2021-09-14 |
Genre | Mathematics |
ISBN | 1000293092 |
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.
Multivalued Linear Operators
Title | Multivalued Linear Operators PDF eBook |
Author | Ronald Cross |
Publisher | CRC Press |
Pages | 356 |
Release | 1998-07-09 |
Genre | Mathematics |
ISBN | 9780824702199 |
Constructs a theoretical framework for the study of linear relations and provides underlying concepts, rules, formulae, theorems and techniques. The book compares the inversion, adjoints, completion and closure of various classes of linear operators. It highlights compact and precompact relations.
Nonlinear Spectral Theory
Title | Nonlinear Spectral Theory PDF eBook |
Author | Jürgen Appell |
Publisher | Walter de Gruyter |
Pages | 420 |
Release | 2004 |
Genre | Mathematics |
ISBN | 3110181436 |
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.
Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras
Title | Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras PDF eBook |
Author | Vladimir Müller |
Publisher | Birkhäuser |
Pages | 390 |
Release | 2013-11-11 |
Genre | Mathematics |
ISBN | 3034877889 |
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.
Spectral Theory of Linear Operators
Title | Spectral Theory of Linear Operators PDF eBook |
Author | Abram Iezekiilovich Plesner |
Publisher | |
Pages | 235 |
Release | 1969 |
Genre | Linear operators |
ISBN |
Spectral Approximation of Linear Operators
Title | Spectral Approximation of Linear Operators PDF eBook |
Author | Francoise Chatelin |
Publisher | SIAM |
Pages | 482 |
Release | 2011-05-26 |
Genre | Mathematics |
ISBN | 0898719992 |
Originally published: New York: Academic Press, 1983.