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Spectral Theory of Multivalued Linear Operators

2021-09-15 Mathematics
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Release : 2021-09-15
Genre : Mathematics
Kind : eBook
Book Rating : 130/5 ( reviews)

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Book Synopsis Spectral Theory of Multivalued Linear Operators by : Aymen Ammar

Download or read book Spectral Theory of Multivalued Linear Operators written by Aymen Ammar. This book was released on 2021-09-15. Available in PDF, EPUB and Kindle. Book excerpt: 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

2021-09-14 Mathematics
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Release : 2021-09-14
Genre : Mathematics
Kind : eBook
Book Rating : 092/5 ( reviews)

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Book Synopsis Spectral Theory of Multivalued Linear Operators by : Aymen Ammar

Download or read book Spectral Theory of Multivalued Linear Operators written by Aymen Ammar. This book was released on 2021-09-14. Available in PDF, EPUB and Kindle. Book excerpt: 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 Linear Operators

1978 Banach spaces
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Release : 1978
Genre : Banach spaces
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Spectral Theory of Linear Operators by : Henry R. Dowson

Download or read book Spectral Theory of Linear Operators written by Henry R. Dowson. This book was released on 1978. Available in PDF, EPUB and Kindle. Book excerpt: General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.

Spectral Theory of Linear Operators

1969 Mathematics
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Release : 1969
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Spectral Theory of Linear Operators by : Abram Iezekiilovich Plesner

Download or read book Spectral Theory of Linear Operators written by Abram Iezekiilovich Plesner. This book was released on 1969. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Spectral Theory

2008-08-22 Mathematics
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Release : 2008-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 262/5 ( reviews)

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Book Synopsis Nonlinear Spectral Theory by : Jürgen Appell

Download or read book Nonlinear Spectral Theory written by Jürgen Appell. This book was released on 2008-08-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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