Skip to main content
Elsevier
View Cart
My account

Books in Operator theory

BooksJournals

    • Random Operator Theory

      • 1st Edition
      • August 4, 2016
      • Reza Saadati
      • English
      • Hardback
        9 7 8 0 1 2 8 0 5 3 4 6 1
      • eBook
        9 7 8 0 0 8 1 0 0 9 5 5 0
      Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications.

    • Dynamical Systems Method for Solving Nonlinear Operator Equations

      • 1st Edition
      • Volume 208
      • September 25, 2006
      • Alexander G. Ramm
      • English
      • Hardback
        9 7 8 0 4 4 4 5 2 7 9 5 0
      • Paperback
        9 7 8 0 4 4 4 5 5 0 8 1 1
      • eBook
        9 7 8 0 0 8 0 4 6 5 5 6 2
      Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author.

    • C<INF>o</INF>-Semigroups and Applications

      • 1st Edition
      • Volume 191
      • March 21, 2003
      • Ioan I. Vrabie
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 2 8 8 8
      • eBook
        9 7 8 0 0 8 0 5 3 0 0 4 8
      The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-l... methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book.The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.

    • Non-Self-Adjoint Boundary Eigenvalue Problems

      • 1st Edition
      • Volume 192
      • June 26, 2003
      • R. Mennicken + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 1 9 2 4
      • Hardback
        9 7 8 0 4 4 4 5 1 4 4 7 9
      • eBook
        9 7 8 0 0 8 0 5 3 7 7 3 3
      This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalentto a first order system, the main techniques are developed for systems. Asymptotic fundamentalsystems are derived for a large class of systems of differential equations. Together with boundaryconditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.The contour integral method and estimates of the resolvent are used to prove expansion theorems.For Stone regular problems, not all functions are expandable, and again relatively easy verifiableconditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such asthe Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.Key features:• Expansion Theorems for Ordinary Differential Equations• Discusses Applications to Problems from Physics and Engineering• Thorough Investigation of Asymptotic Fundamental Matrices and Systems• Provides a Comprehensive Treatment• Uses the Contour Integral Method• Represents the Problems as Bounded Operators• Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions

    • Operator Theory and Numerical Methods

      • 1st Edition
      • Volume 30
      • July 3, 2001
      • H. Fujita + 2 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 4 6 7 3 9
      • Hardback
        9 7 8 0 4 4 4 5 0 4 7 4 6
      • eBook
        9 7 8 0 0 8 0 5 3 8 0 2 0
      In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true.

    • General Theory of C*-Algebras

      • 1st Edition
      • Volume 3
      • July 11, 2001
      • English
      • Paperback
        9 7 8 0 4 4 4 5 4 2 1 9 9
      • eBook
        9 7 8 0 0 8 0 5 2 8 3 4 2

    • The Theory of Fractional Powers of Operators

      • 1st Edition
      • Volume 187
      • January 17, 2001
      • C. Martinez + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 4 2 1 3 7
      • eBook
        9 7 8 0 0 8 0 5 1 9 0 7 4
      This book makes available to researchers and advanced graduates a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis. For the first time ever, a book deals with this subject monographically, despite the large number of papers written on it during the second half of the century. The first chapters are concerned with the construction of a basic theory of fractional powers and study the classic questions in that respect. A new and distinct feature is that the approach adopted has allowed the extension of this theory to locally convex spaces, thereby including certain differential operators, which appear naturally in distribution spaces. The bulk of the second part of the book is dedicated to powers with pure imaginary exponents, which have been the focus of research in recent years, ever since the publication in 1987 of the now classic paper by G.Dore and A.Venni. Special care has been taken to give versions of the results with more accurate hypotheses, particularly with respect to the density of the domain or the range of the operator. The authors have made a point of making the text clear and self-contained. Accordingly, an extensive appendix contains the material on real and functional analysis used and, at the end of each chapter there are detailed historical and bibliographical notes in order to understand the development and current state of research into the questions dealt with.

    • Banach Spaces

      • 1st Edition
      • Volume 1
      • April 30, 2001
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 7 4 9 5
      • Paperback
        9 7 8 0 4 4 4 5 4 6 7 9 1
      • eBook
        9 7 8 0 0 8 0 5 2 8 3 7 3

    • Hilbert Spaces

      • 1st Edition
      • Volume 4
      • July 11, 2001
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 1 8 2 5
      • Hardback
        9 7 8 0 4 4 4 5 0 7 5 2 5
      • eBook
        9 7 8 0 0 8 0 5 2 8 3 5 9
      This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of “Definition – Theorem – Proof - Example - Exercises”. The proofs are rather thorough and there many examples. The first part of the book(the first three chapters, resp. the first two volumes) is devoted to the theory of Banach spaces in the most general sense of the term. The purpose of the first chapter (resp. first volume) is to introduce those results on Banach spaces which are used later or which are closely connected with the book. It therefore only contains a small part of the theory, and several results are stated (and proved) in a diluted form. The second chapter (which together with Chapter 3 makes the second volume) deals with Banach algebras (and involutive Banach algebras), which constitute the main topic of the first part of the book. The third chapter deals with compact operators on Banach spaces and linear (ordinary and partial) differential equations - applications of the, theory of Banach algebras.