傅立叶级数

出版时间：2003-11  出版社：北京 世界图书出版公司  作者：R.E.Edwards  页数：369  
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内容概要

Apart from a number of minor corrections and changes, a substantial reformulation and up-dating of Chapters 14 and 15 has taken place. This reformulation and up-dating is a major and very welcome contribution from my friend and colleague, Dr J.W. Sanders, to whom I express my sincere thanks. His efforts have produced a much better result than I could have achieved on my own. Warm thanks are also due to Dr Jo Ward, Who checked some of the revised material. New Sections 16.9 and 16.10 have also been added. The bibliography has been expanded and brought up to date, though it is still not exhaustive. In spite of these changes, the third paragraph in the Preface to the revised edition of Volume I is applicable here. What has been aeeomplished here is not a complete account of developments over the past 15 years; such an account would require many volumes. Even so, it may assist some readers who wish to appraise some of these developments. More ambitious readers should consult Mathematical Reviews from around Volume 50 onwards.

书籍目录

Chapter 11 SPANS OF TRANSLATES. CLOSED IDEALS. CLOSED SUBALGEBRAS. BANACH ALGEBRAS   11.1 Closed Invariant Subspaces and Closed Ideals   11.2 The Structure of Closed Ideals and Related Topics   11.3 Closed Subalgebras   11.4 Banach Algebras and Their Applications   Exercises Chapter 12 DISTRIBUTIONS AND MEASURES   12.1 Concerning CD   12.2 Definition and Examples of Distributions and Measures   12.3 Convergence of Distributions   12.4 Differentiation of Distributions   12.5 Fourier Coefficients and Fourier Series of Distributions   12.6 Convolutions of Distributions   12.7 More about M and Lp   12.8 Hilbert‘s Distribution and Conjugate Series   12.9 The Theorem of Marcel Riesz   12.10 Mean Convergence of Fourier Series in Lp (1 < p < oo)   12.11 Pseudomeasures and Their Applications   12.12 Capacities and Beurling‘s Problem   12.13 The Dual Fomr of Bochner's Theorem  ExercisesChapter 13 INTEROPLATION THEOREMSChapter 14 CHANGING SIGNS OF FOURIER COEFICIENTSChapter 15 LACUNARY FOURIER SERIESChapter 16 MULTIPLIERSBibliographyResearch PublicationsCorrigenda to 2nd(Revised)Edition of Volume 1SymbolsIndex