Functional Analysis

An Introductory Course

Sergei Ovchinnikov (Autor)

Buch | Softcover

XII, 205 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-91511-1 (ISBN)

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This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Boundedness Theorem, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text.

Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.

Sergei Ovchinnikov is Professor Emeritus of Mathematics at San Francisco State University. His other Universitext books are Measure, Integral, Derivative: a Course on Lebesgue's Theory (2013) and Graphs and Cubes (2011).

Preface.- 1. Preliminaries.- 2. Metric Spaces.- 3. Special Spaces.- 4. Normed Spaces.- 5. Linear Functionals.- 6. Fundamental Theorems.- 7. Hilbert Spaces.- A. Hilbert Spaces L2(J).- References.- Index.

"This textbook is well organized and the proofs are carefully written. ... Each chapter is concluded with an interesting note and several exercises, helping the reader to better understand the topics of the chapter. ... it will be useful for upper-undergraduate and beginning graduate students." (Mohammad Sal Moslehian, zbMATH 1398.46001, 2018)

“This textbook is well organized and the proofs are carefully written. … Each chapter is concluded with an interesting note and several exercises, helping the reader to better understand the topics of the chapter. … it will be useful for upper-undergraduate and beginning graduate students.” (Mohammad Sal Moslehian, zbMATH 1398.46001, 2018)

Erscheinungsdatum	03.07.2018
Reihe/Serie	Universitext
Zusatzinfo	XII, 205 p. 13 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	340 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Banach space • Functional analysis textbook • Fundamental theorems of functional analysis • Hahn-Banach theorem • hilbert space • Inner product space • Introductory functional analysis • normed space • Summable families
ISBN-10	3-319-91511-8 / 3319915118
ISBN-13	978-3-319-91511-1 / 9783319915111
Zustand	Neuware