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Books in Functional analysis

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Theory of Approximate Functional Equations

  • 1st Edition
  • February 23, 2016
  • Madjid Eshaghi Gordji + 1 more
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 8 0 3 9 2 0 - 5
  • eBook
    9 7 8 - 0 - 1 2 - 8 0 3 9 7 1 - 7
Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stability of a functional equation implies this completeness, has been investigated by several authors. In this book the authors investigate these developments in the theory of approximate functional equations.

Solution of Equations and Systems of Equations

  • 2nd Edition
  • February 17, 2016
  • A. M. Ostrowski
  • Paul A. Smith + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 2 3 6 4 - 3
Solution of Equations and Systems of Equations, Second Edition deals with the Laguerre iteration, interpolating polynomials, method of steepest descent, and the theory of divided differences. The book reviews the formula for confluent divided differences, Newton's interpolation formula, general interpolation problems, and the triangular schemes for computing divided differences. The text explains the method of False Position (Regula Falsi) and cites examples of computation using the Regula Falsi. The book discusses iterations by monotonic iterating functions and analyzes the connection of the Regula Falsi with the theory of iteration. The text also explains the idea of the Newton-Raphson method and compares it with the Regula Falsi. The book also cites asymptotic behavior of errors in the Regula Falsi iteration, as well as the theorem on the error of the Taylor approximation to the root. The method of steepest descent or gradient method proposed by Cauchy ensures "global convergence" in very general conditions. This book is suitable for mathematicians, students, and professor of calculus, and advanced mathematics.

Numerical Solutions of Three Classes of Nonlinear Parabolic Integro-Differential Equations

  • 1st Edition
  • November 4, 2015
  • T Jangveladze + 2 more
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 8 0 4 6 2 8 - 9
  • eBook
    9 7 8 - 0 - 1 2 - 8 0 4 6 6 9 - 2
This book describes three classes of nonlinear partial integro-differential equations. These models arise in electromagnetic diffusion processes and heat flow in materials with memory. Mathematical modeling of these processes is briefly described in the first chapter of the book. Investigations of the described equations include theoretical as well as approximation properties. Qualitative and quantitative properties of solutions of initial-boundary value problems are performed therafter. All statements are given with easy understandable proofs. For approximate solution of problems different varieties of numerical methods are investigated. Comparison analyses of those methods are carried out. For theoretical results the corresponding graphical illustrations are included in the book. At the end of each chapter topical bibliographies are provided.

Tables of the Function w (z)- e-z2 ? ex2 dx

  • 1st Edition
  • July 3, 2014
  • K. A. Karpov
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 1 4 5 7 - 3
Tables of the Function w(z) = e-z2 z?0ex2dx in the Complex Domain contains tables of the function in connection with the problem of the radio wave propagation. These tables are compiled in the Experimental-Computing Laboratories of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The function w(z) is represented in the upper half-plane by the asymptotic series. Description of the tables and method of computation is provided. This book will prove useful to mathematicians and researchers.

Convexity Theory and its Applications in Functional Analysis

  • 1st Edition
  • June 28, 2014
  • L. Asimow
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 4 6 9 - 8
Convexity Theory and its Applications in Functional Analysis is a five-chapter text that provides a geometric perspective of the convexity theory and its practical applications. Chapter 1 reviews the functional analytic preliminaries, including the Krein-Smulyan Theorem, the basic Choquet Theory, and the Bishop-Phelps Theorem. Chapter 2 gives the basic duality results, lattice theory and concrete representation theorems for order unit spaces and Banach lattices of type Mand L. Chapters 3 and 4 deal with the real affine function spaces through examining the Choquet simplex and the application of the study of real A(K) spaces to complex-values function spaces by means of a complex state space. Chapter 5 highlights the application of the theory to the study of non-commutative Banach algebras. This book will prove useful to mathematicians, engineers, and physicists.

Subharmonic Functions

  • 1st Edition
  • Volume 2
  • June 28, 2014
  • W. K. Hayman
  • P. M. Cohn + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 6 1 8 - 0
Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable. The material also has applications in differential equations and differential equations and differential geometry. It reflects the increasingly important role that subharmonic functions play in these areas of mathematics. The presentation goes back to the pioneering work of Ahlfors, Heins, and Kjellberg, leading to and including the more recent results of Baernstein, Weitsman, and many others. The volume also includes some previously unpublished material. It addresses mathematicians from graduate students to researchers in the field and will also appeal to physicists and electrical engineers who use these tools in their research work. The extensive preface and introductions to each chapter give readers an overview. A series of examples helps readers test their understatnding of the theory and the master the applications.

Generalized Functions

  • 1st Edition
  • May 12, 2014
  • I. M. Gel'fand + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 6 2 2 4 - 6
Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.

Methods of Functional Analysis for Application in Solid Mechanics

  • 1st Edition
  • Volume 9
  • October 22, 2013
  • J. Mason
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 8 9 9 1 - 5
Publications oriented to the interests of engineering scientists and graduate students on topics of functional analysis and its applications are rare - this book has been written to fill the gap in the literature. It provides a readable account of basic mathematic topics, with illustrative examples and chapters devoted to finite elements, variational principles of elasticity and plasticity, variational inequalities and elastic stability. The text is entirely self-contained and covers a wide range of topics and ideas, from elementary concepts to modern theories and applications, and includes numerous references. It is written for engineers, graduate students and researchers who need a general knowledge of modern mathematical methods in solid mechanics.

Aspects of Positivity in Functional Analysis

  • 1st Edition
  • Volume 122
  • October 10, 2011
  • R. Nagel + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 3 3 - 9
The contributions collected in this volume exhibit the increasingly wide spectrum of applications of abstract order theory in analysis and show the possibilities of order-theoretical argumentation.The following areas are discussed: potential theory, partial differential operators of second order, Schrodinger operators, theory of convexity, one-parameter semigroups, Lie algebras, Markov processes, operator-algebras, noncommutative integration and geometry of Banach spaces.