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Linear Operators and Their Essential Pseudospectra

2018-04-17 Mathematics
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Release : 2018-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 25X/5 ( reviews)

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Book Synopsis Linear Operators and Their Essential Pseudospectra by : Aref Jeribi

Download or read book Linear Operators and Their Essential Pseudospectra written by Aref Jeribi. This book was released on 2018-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Linear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.

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 and Applications of Linear Operators and Block Operator Matrices

2015-07-04 Science
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Release : 2015-07-04
Genre : Science
Kind : eBook
Book Rating : 661/5 ( reviews)

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Book Synopsis Spectral Theory and Applications of Linear Operators and Block Operator Matrices by : Aref Jeribi

Download or read book Spectral Theory and Applications of Linear Operators and Block Operator Matrices written by Aref Jeribi. This book was released on 2015-07-04. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectra and Pseudospectra

2005-08-07 Mathematics
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Release : 2005-08-07
Genre : Mathematics
Kind : eBook
Book Rating : 465/5 ( reviews)

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Book Synopsis Spectra and Pseudospectra by : Lloyd N. Trefethen

Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen. This book was released on 2005-08-07. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

S-Essential Spectra and the Weyl Pseudospectra of Linear Operators

2015-10-22
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Release : 2015-10-22
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Kind : eBook
Book Rating : 127/5 ( reviews)

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Book Synopsis S-Essential Spectra and the Weyl Pseudospectra of Linear Operators by : Ammar Aymen

Download or read book S-Essential Spectra and the Weyl Pseudospectra of Linear Operators written by Ammar Aymen. This book was released on 2015-10-22. Available in PDF, EPUB and Kindle. Book excerpt: In this work we present a spectral study of semi regular operator. The concept of semi regularity and essentially semi regularity amongst the various concepts of regularity originating from Fredholm theory, and we introduce new notions and unprecedented denition to develop pseudospectral theory. We built our denition on the basis of essential spectra and tried to comply it with pseudospectral theory. So, we intend to obtain what we call "Weyl pseudospectra."

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