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A Guide to Functional Analysis /
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 spec...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
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| Colección: | Dolciani mathematical expositions.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.