初歩の関数解析（テキスト）<br>Beginning Functional Analysis (Undergraduate Texts in Mathematics) （2002. XI, 197 p. w. figs. 24 cm）

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初歩の関数解析（テキスト）
Beginning Functional Analysis (Undergraduate Texts in Mathematics) （2002. XI, 197 p. w. figs. 24 cm）

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  • 製本 Hardcover:ハードカバー版／ページ数 210 p.
  • 商品コード 9780387952246

基本説明

For a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts. Contents: Metric Spaces, Normed Spaces, Inner Product Spaces; The Topology of Metric Spaces; Measure and Integration; and more.

Full Description

This book is designed as a text for a first course on functional analysis for ad­ vanced undergraduates or for beginning graduate students. It can be used in the undergraduate curriculum for an honors seminar, or for a "capstone" course. It can also be used for self-study or independent study. The course prerequisites are few, but a certain degree of mathematical sophistication is required. A reader must have had the equivalent of a first real analysis course, as might be taught using [25] or [109], and a first linear algebra course. Knowledge of the Lebesgue integral is not a prerequisite. Throughout the book we use elementary facts about the complex numbers; these are gathered in Appendix A. In one spe­ cific place (Section 5.3) we require a few properties of analytic functions. These are usually taught in the first half of an undergraduate complex analysis course. Because we want this book to be accessible to students who have not taken a course on complex function theory, a complete description of the needed results is given. However, we do not prove these results.

Contents

Introduction: To the Student.- 1 Metric Spaces, Normed Spaces, Inner Product Spaces.- 2 The Topology of Metric Spaces.- 3 Measure and Integration.- 4 Fourier Analysis in Hilbert Space.- 5 An Introduction to Abstract Linear Operator Theory.- 6 Further Topics.- A Complex Numbers.- Exercises for Appendix A.- B Basic Set Theory.- Exercises for Appendix B.- References.