Linear Operator Equations: Approximation And Regularization
Linear Operator Equations: Approximation And Regularization

Author: M Thamban Nair

Publisher: World Scientific

Published: 2009-05-05

Total Pages: 264

ISBN-13: 981446967X

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Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.

Analysis as a Tool in Mathematical Physics
Analysis as a Tool in Mathematical Physics

Author: Pavel Kurasov

Publisher: Springer Nature

Published: 2020-07-14

Total Pages: 627

ISBN-13: 3030315312

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Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications”, held in Stockholm, Sweden, in March 2016, and “Operator Theory, Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.

Semigroups of Linear Operators and Applications to Partial Differential Equations
Semigroups of Linear Operators and Applications to Partial Differential Equations

Author: Amnon Pazy

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 289

ISBN-13: 1461255619

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Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Traces and Determinants of Linear Operators
Traces and Determinants of Linear Operators

Author: Israel Gohberg

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 261

ISBN-13: 303488401X

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This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.

Spectral Theory and Applications of Linear Operators and Block Operator Matrices
Spectral Theory and Applications of Linear Operators and Block Operator Matrices

Author: Aref Jeribi

Publisher: Springer

Published: 2015-07-04

Total Pages: 608

ISBN-13: 3319175661

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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.

Unbounded Linear Operators
Unbounded Linear Operators

Author: Seymour Goldberg

Publisher: Courier Corporation

Published: 2006-01-01

Total Pages: 212

ISBN-13: 0486453316

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This volume presents a systematic treatment of the theory of unbounded linear operators in normed linear spaces with applications to differential equations. Largely self-contained, it is suitable for advanced undergraduates and graduate students, and it only requires a familiarity with metric spaces and real variable theory. After introducing the elementary theory of normed linear spaces--particularly Hilbert space, which is used throughout the book--the author develops the basic theory of unbounded linear operators with normed linear spaces assumed complete, employing operators assumed closed only when needed. Other topics include strictly singular operators; operators with closed range; perturbation theory, including some of the main theorems that are later applied to ordinary differential operators; and the Dirichlet operator, in which the author outlines the interplay between functional analysis and "hard" classical analysis in the study of elliptic partial differential equations. In addition to its readable style, this book's appeal includes numerous examples and motivations for certain definitions and proofs. Moreover, it employs simple notation, eliminating the need to refer to a list of symbols.

Linear Operators for Quantum Mechanics
Linear Operators for Quantum Mechanics

Author: Thomas F. Jordan

Publisher: Courier Corporation

Published: 2012-09-20

Total Pages: 162

ISBN-13: 0486140547

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Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.

Linear Functional Equations. Operator Approach
Linear Functional Equations. Operator Approach

Author: Anatolij Antonevich

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 188

ISBN-13: 3034889771

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In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ ual representatives are related with problems arising in various areas of mathemat ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au tomorphisms of Banach algebras, and other problems.