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Cover: 9783540586548 | Functional Analysis | Kösaku Yosida | Taschenbuch | Paperback | 1995
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Functional Analysis
Taschenbuch von Kösaku Yosida
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor

Biography of Kôsaku Yosida

Kôsaku Yosida (7.2.1909-20.6.1990) was born in Hiroshima, Japan. After studying mathematics a the University of Tokyo he held posts at Osaka and Nagoya Universities before returning to the University of Tokyo in 1955.

Yosida obtained important and fundamental results in functional analysis and probability. He is best remembered for his joint work with E. Hille which brought forth a theory of semigroups of operators successfully applied to diffusion equations, Markov processes, hyperbolic equations and potential theory. His famous textbook on Functional Analysis was published in 6 distinct editions between 1965 and 1980.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1995
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 516
Reihe: Classics in Mathematics
Inhalt: xvi
504 S.
ISBN-13: 9783540586548
ISBN-10: 3540586547
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Yosida, Kösaku
Auflage: 6th ed. 1995
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Classics in Mathematics
Maße: 235 x 155 x 28 mm
Von/Mit: Kösaku Yosida
Erscheinungsdatum: 15.02.1995
Gewicht: 0,774 kg
preigu-id: 106694007
Über den Autor

Biography of Kôsaku Yosida

Kôsaku Yosida (7.2.1909-20.6.1990) was born in Hiroshima, Japan. After studying mathematics a the University of Tokyo he held posts at Osaka and Nagoya Universities before returning to the University of Tokyo in 1955.

Yosida obtained important and fundamental results in functional analysis and probability. He is best remembered for his joint work with E. Hille which brought forth a theory of semigroups of operators successfully applied to diffusion equations, Markov processes, hyperbolic equations and potential theory. His famous textbook on Functional Analysis was published in 6 distinct editions between 1965 and 1980.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1995
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 516
Reihe: Classics in Mathematics
Inhalt: xvi
504 S.
ISBN-13: 9783540586548
ISBN-10: 3540586547
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Yosida, Kösaku
Auflage: 6th ed. 1995
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Classics in Mathematics
Maße: 235 x 155 x 28 mm
Von/Mit: Kösaku Yosida
Erscheinungsdatum: 15.02.1995
Gewicht: 0,774 kg
preigu-id: 106694007
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