A guide to functional analysis [[electronic resource] /] / Steven G. Krantz

• Autore: Krantz Steven G (Steven George), <1951->
• Pubblicazione: Washington, D.C., : Mathematical Association of America, 2013
• Descrizione fisica: 1 online resource (0 p.)
• Disciplina: 515.7
• Soggetto topico: Functional analysis
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: cover ; copyright page ; title page ; Contents; Preface; Fundamentals; What is Functional Analysis?; Normed Linear Spaces; Finite-Dimensional Spaces; Linear Operators; The Baire Category Theorem; The Three Big Results; Applications of the Big Three; Ode to the Dual Space; Introduction; Consequences of the Hahn-Banach Theorem; Hilbert Space; Introduction; The Geometry of Hilbert Space; The Algebra of Operators; Preliminaries; The Algebra of Bounded Linear Operators; Compact Operators; Banach Algebra Basics; Introduction to Banach Algebras; The Structure of a Banach Algebra; Ideals ; The Wiener Tauberian TheoremTopological Vector Spaces; Basic Ideas; Fréchet Spaces; Distributions; Preliminary Remarks; What is a Distribution?; Operations on Distributions; Approximation of Distributions; The Fourier Transform; Spectral Theory; Background; The Main Result; Convexity; Introductory Thoughts; Separation Theorems; The Main Result; Fixed-Point Theorems; Banach's Theorem; Two Applications; The Schauder Theorem; Table of Notation; Glossary; Bibliography; Index; About the Author
• Sommario/riassunto: The purpose of A Guide to Functional Analysis is to introduce the reader with minimal background to the basic scripture of functional analysis. Readers should know some real analysis and some linear algebra. Measure theory rears its ugly head in some of the examples and also in the treatment of spectral theory. The latter is unavoidable and the former allows us to present a rich variety of examples. The nervous reader may safely skip any of the measure theory and still derive a lot from the rest of the book. Apart from this caveat, the book is almost completely self-contained; in a few instances we mention easily accessible references. A feature that sets this book apart from most other functional analysis texts is that it has a lot of examples and a lot of applications. This helps to make the material more concrete, and relates it to ideas that the reader has already seen. It also makes the book more accessible to a broader audience.
• Titolo autorizzato: A guide to functional analysis
• ISBN: 1-61444-213-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910462876503321
• Lo trovi qui: Univ. Federico II
• Serie: Dolciani Mathematical Expositions