Beginning Functional Analysis

1. Auflage. Softcover version of original hardcover Auflage 2002
ISBN: 978-1-4419-2914-3
Verlag: Springer

Buch, Englisch, 197 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 335 g

Reihe: Undergraduate Texts in Mathematics

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Saxe, Karen

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.

Über Autor(innen)

Saxe, Karen
Karen Saxe is Associate Professor of Mathematics at Macalester College in St. Paul, Minnesota. She received her Ph.D. from the University of Oregon. Before joining the faculty at Macalester, she held a two-year FIPSE post-doctoral position at St. Olaf College in Northfield, Minnesota. She currently serves on the editorial board of the MAA's College Mathematics Journal. This is her first book.