Functional Analysis / by Kôsaku Yosida
(Classics in Mathematics ; 123)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 1995 |
| 本文言語 | 英語 |
| 大きさ | XVI, 504 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Yosida, Kôsaku author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Functional analysis FREE:Mathematics FREE:Functional Analysis |
| 分 類 | DC23:515.7 |
| 巻冊次 | ISBN:9783642618598 
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| ISBN | 9783642618598 |
| URL | http://dx.doi.org/10.1007/978-3-642-61859-8 |
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