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Catalogue Information
Field name	Details
Dewey Class	515.7
Title	Functional Analysis ([EBook]) / by Kôsaku Yosida.
Author	Yosida, Kôsaku. , 1909-1990
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1995.
Physical Details	XVI, 504 pages : online resource.
Series	Classics in mathematics 1431-0821 ; ; 123
ISBN	9783642618598
Summary Note	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.:
Contents note	0. Preliminaries -- I. Semi-norms -- II. Applications of the Baire-Hausdorff Theorem -- III. The Orthogonal Projection and F. Riesz’ Representation Theorem -- IV. The Hahn-Banach Theorems -- V. Strong Convergence and Weak Convergence -- VI. Fourier Transform and Differential Equations -- VII. Dual Operators -- VIII. Resolvent and Spectrum -- IX. Analytical Theory of Semi-groups -- X. Compact Operators -- XI. Normed Rings and Spectral Representation -- XII. Other Representation Theorems in Linear Spaces -- XIII. Ergodic Theory and Diffusion Theory -- XIV. The Integration of the Equation of Evolution -- Supplementary Notes -- Notation of Spaces.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-61859-8
Links to Related Works	Subject References: Functional Analysis . Mathematics . Authors: Yosida, Kôsaku. 1909-1990 . Yosida, Kôsaku, 1909-1990. . Corporate Authors: SpringerLink (Online service) . Series: Classics in mathematics . Classification: 515.7 .

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Functional Analysis

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