Functional Analysis / by Kôsaku Yosida
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 1965 |
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| 書誌ID | OB00847458 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 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. License restrictions may limit access Summary: Thepresent book is based on lectures given by theauthor at the University ofTokyo during the past ten years. It is intended as a textbooktobestudiedbystudents ontheirownortobeusedinacourse on Functional Analysis, i. e. , the generaltheory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessaryprerequisitesforthereadingofthisbookaresummarized, with or without proof, in Chapter 0 under titles: Set Theory,Topo logical Spaces,MeasureSpacesand Linear Spaces. Then,startingwith the chapter on Semi-norms, a general theory of Banach and Hilbert spacesispresentedinconnectionwiththetheoryofgeneralizedfunctions ofS. L. SOBOLEVandL. SCHWARTZ. Whilethebookisprimarilyaddressed tograduatestudents,itishopedit mightproveusefultoresearchmathe maticians, both pure and applied. The reader may pass e. g. from ChapterIX(AnalyticalTheoryofSemi-groups)directlytoChapterXIII (ErgodicTheoryandDiffusionTheory)andtoChapterXIV(Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented inthe form of theappendices to ChapterVand ChapterX, respectively. These mightbeskipped forthefirst readingbythosewho areinterestedratherintheapplicationoflinearoperators. In the preparation of the present book, the author has received valuable advice and criticism from many friends. Especially, Mrs, K. HILLEhaskindlyreadthroughthemanuscript aswellasthegalley and page proofs. Without her painstaking help, this book could not have been printed in the present style in the language which was not spoken to the author in the cradle. The author owes very much to his old friends, Professor E. HILLE and Professor S. KAKUTANI of YaleUniversityandProfessorR. S. PHILLIPSofStanfordUniversityfor thechanceto stay in their universities in 1962, which enabled him to polishthegreaterpartofthemanuscript ofthisbook,availing himself of their valuable advice. Professor S. ITOand Dr. H |
| 著者標目 | *Yosida, Kôsaku SpringerLink (Online service) |
| 統一書名標目 | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete, |
| 件 名 | LCSH:Mathematics LCSH:Computer science LCSH:Topology FREE:Mathematics FREE:Topology FREE:Arithmetic and Logic Structures |
| 分 類 | LCC:QA611-614.97 DC23:514 |
| 巻冊次 | ISBN:9783662257623 RefWorks出力（各巻） print ; ISBN:9783662236758 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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