Functional Analysis

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe maticians, both pure and applied. The reader may pass, e. g. , from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

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  • Author : Kösaku Yosida
  • Publisher : Springer Science & Business Media
  • Pages : 504 pages
  • ISBN : 3642618596
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKFunctional Analysis

Functional Analysis

Functional Analysis
  • Author : Kösaku Yosida
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKFunctional Analysis

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are

Functional Analysis

Functional Analysis
  • Author : Peter D. Lax
  • Publisher : John Wiley & Sons
  • Release : 28 August 2014
GET THIS BOOKFunctional Analysis

Includes sections on the spectral resolution and spectralrepresentation of self adjoint operators, invariant subspaces,strongly continuous one-parameter semigroups, the index ofoperators, the trace formula of Lidskii, the Fredholm determinant,and more. * Assumes prior knowledge of Naive set theory, linear algebra,point set topology, basic complex variable, and realvariables. * Includes an appendix on the Riesz representation theorem.

Functional Analysis

Functional Analysis
  • Author : Robert E. Edwards
  • Publisher : Courier Corporation
  • Release : 01 January 1995
GET THIS BOOKFunctional Analysis

Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.

Introduction to Functional Analysis

Introduction to Functional Analysis
  • Author : Christian Clason
  • Publisher : Birkhäuser
  • Release : 01 December 2020
GET THIS BOOKIntroduction to Functional Analysis

Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert

Problems in Real and Functional Analysis

Problems in Real and Functional Analysis
  • Author : Alberto Torchinsky
  • Publisher : American Mathematical Soc.
  • Release : 14 December 2015
GET THIS BOOKProblems in Real and Functional Analysis

It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and

A First Look at Numerical Functional Analysis

A First Look at Numerical Functional Analysis
  • Author : W. W. Sawyer
  • Publisher : Courier Dover Publications
  • Release : 22 December 2010
GET THIS BOOKA First Look at Numerical Functional Analysis

Functional analysis arose from traditional topics of calculus and integral and differential equations. This accessible text by an internationally renowned teacher and author starts with problems in numerical analysis and shows how they lead naturally to the concepts of functional analysis. Suitable for advanced undergraduates and graduate students, this book provides coherent explanations for complex concepts. Topics include Banach and Hilbert spaces, contraction mappings and other criteria for convergence, differentiation and integration in Banach spaces, the Kantorovich test for convergence

Functional Analysis, Calculus of Variations and Optimal Control

Functional Analysis, Calculus of Variations and Optimal Control
  • Author : Francis Clarke
  • Publisher : Springer Science & Business Media
  • Release : 06 February 2013
GET THIS BOOKFunctional Analysis, Calculus of Variations and Optimal Control

Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well

Functional Analysis

Functional Analysis
  • Author : Joseph Muscat
  • Publisher : Springer
  • Release : 23 July 2014
GET THIS BOOKFunctional Analysis

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum

Nonlinearity and Functional Analysis

Nonlinearity and Functional Analysis
  • Author : Melvyn S. Berger
  • Publisher : Academic Press
  • Release : 27 October 1977
GET THIS BOOKNonlinearity and Functional Analysis

Nonlinearity and Functional Analysis is a collection of lectures that aim to present a systematic description of fundamental nonlinear results and their applicability to a variety of concrete problems taken from various fields of mathematical analysis. For decades, great mathematical interest has focused on problems associated with linear operators and the extension of the well-known results of linear algebra to an infinite-dimensional context. This interest has been crowned with deep insights, and the substantial theory that has been developed has

A First Course in Functional Analysis

A First Course in Functional Analysis
  • Author : Orr Moshe Shalit
  • Publisher : CRC Press
  • Release : 16 March 2017
GET THIS BOOKA First Course in Functional Analysis

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside

A Friendly Approach to Functional Analysis

A Friendly Approach to Functional Analysis
  • Author : Amol Sasane
  • Publisher : World Scientific Publishing Company
  • Release : 20 February 2017
GET THIS BOOKA Friendly Approach to Functional Analysis

This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes

Aspects of Positivity in Functional Analysis

Aspects of Positivity in Functional Analysis
  • Author : R. Nagel,U. Schlotterbeck,M.P.H. Wolff
  • Publisher : Elsevier
  • Release : 10 October 2011
GET THIS BOOKAspects of Positivity in Functional Analysis

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.