Spectral Theory And Applications Of Linear Operators And Block Operator Matrices
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Spectral Theory And Applications Of Linear Operators And Block Operator Matrices
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Author : Aref Jeribi
language : en
Publisher:
Release Date : 2015
Spectral Theory And Applications Of Linear Operators And Block Operator Matrices written by Aref Jeribi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.
Spectral Theory Of Block Operator Matrices And Applications
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Author : Christiane Tretter
language : en
Publisher: Imperial College Press
Release Date : 2008
Spectral Theory Of Block Operator Matrices And Applications written by Christiane Tretter and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics.
Spectral Theory And Applications Of Linear Operators And Block Operator Matrices
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Author : Aref Jeribi
language : en
Publisher: Springer
Release Date : 2015-07-04
Spectral Theory And Applications Of Linear Operators And Block Operator Matrices written by Aref Jeribi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-04 with Science categories.
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.
Spectral Theory Of Block Operator Matrices And Applications
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Author : Christiane Tretter
language : en
Publisher: World Scientific
Release Date : 2008
Spectral Theory Of Block Operator Matrices And Applications written by Christiane Tretter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This book presents new concepts in operator theory and covers classes of operators (in particular, non-selfadjoint operators) which exhibit various interesting phenomena. Special attention is paid to applications in many areas of mathematical physics, including quantum mechanics, fluid mechanics, and magnetohydrodynamics.The author also discusses an operator theoretic approach to spectral problems for linear operators admitting a certain block structure. The results apply to bounded or finite-dimensional operators like block matrices as well to unbounded operators describing systems of differential equations. New concepts of numerical range are developed.
Spectral Theory For Linear Operators
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Author : Bilel Krichen
language : en
Publisher: CRC Press
Release Date : 2025-08-01
Spectral Theory For Linear Operators written by Bilel Krichen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-01 with Mathematics categories.
This book focuses on spectral theory for linear operators involving bounded or unbounded demicompact linear operators acting on Banach spaces. This class played an important rule in the theory of perturbation. More precisely, it contributed in the construction of several classes of stability of essential spectra for bounded or unbounded linear operators. We should emphasize that this book is the first one dealing with the demicompactness concept and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. Researchers, as well as graduate students in applicable analysis, will find that this book constitutes a useful survey of the fundamental principles of the subject. Nevertheless, the reader is assumed to be, at least, familiar with some related sections concerning notions like the compact, Fredholm operators, the basic tools of the weak topology, the concept of measures of weak noncompactness, etc. Otherwise, the reader is urged to consult the recommended literature in order to benefit fully from this book. Features - • First book dealing with demicompactness theory and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. • Self-contained coverage of classical and more recent classes of perturbations involving the concept of demicompactness. • Offers a useful survey of the fundamental principles of spectral theory. • Provides applications for problem arising in physics and which are modeled by integral or partial differential equations.
Spectral Theory Of Multivalued Linear Operators
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Author : Aymen Ammar
language : en
Publisher: CRC Press
Release Date : 2021-09-15
Spectral Theory Of Multivalued Linear Operators written by Aymen Ammar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-15 with Mathematics categories.
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.
Problems In Finite Element Methods
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2024-11-01
Problems In Finite Element Methods written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
This book discusses major topics and problems in finite element methods. It is targeted to graduate students and researchers in applied mathematics, physics, and engineering, wishing to learn and familiarize themselves with finite element theory. The book describes the nodal method for squares or rectangles and triangles, as well as an increase of the error between exact solution and approximate solution. It discusses an approximation of positive symmetric first-order systems in the Friedrichs sense by finite element methods. In addition, the book also explains the continuous and discontinuous approximation methods, adapted to the structure of the transport equation, leading to linear systems of quasi-explicit resolution, and therefore commonly used in practice.
Perturbation Theory For Linear Operators
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2021-07-28
Perturbation Theory For Linear Operators written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-28 with Mathematics categories.
This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
Advanced Functional Analysis
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Author : Eberhard Malkowsky
language : en
Publisher: CRC Press
Release Date : 2019-02-25
Advanced Functional Analysis written by Eberhard Malkowsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-25 with Mathematics categories.
Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research.
Linear Operators And Their Essential Pseudospectra
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Author : Aref Jeribi
language : en
Publisher: CRC Press
Release Date : 2018-04-17
Linear Operators And Their Essential Pseudospectra written by Aref Jeribi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-17 with Mathematics categories.
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.