Beginning Functional Analysis
Seiten
2010
|
Softcover reprint of hardcover 1st ed. 2002
Springer-Verlag New York Inc.
978-1-4419-2914-3 (ISBN)
Springer-Verlag New York Inc.
978-1-4419-2914-3 (ISBN)
This book is designed as a text for a first course on functional analysis for ad vanced undergraduates or for beginning graduate students. 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.
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.
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.
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.
| Erscheint lt. Verlag | 3.12.2010 |
|---|---|
| Reihe/Serie | Undergraduate Texts in Mathematics |
| Zusatzinfo | XI, 197 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4419-2914-2 / 1441929142 |
| ISBN-13 | 978-1-4419-2914-3 / 9781441929143 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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