Elements of Functional Analysis

Description

This is a graduate text on functional analysis. After presenting the fundamental function spaces and their duals, the authors study topics in operator theory and finally develop the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Along the way, the reader is presented with a truly remarkable assortment of well formulated and interesting exercises, which test the understanding as well as point out many related topics. The answers and hints that are not already contained in the statements of the exercises are collected at the end of the book.;I. Function Spaces and Their Duals: The Space of Continous Functions on a Compact Set -- Locally Compact Spaces and Radon Measures -- Hilbert Spaces -- Lp Spaces; II. Operators: Spectra -- Compact Operators; III. Distributions: Definitions and Examples -- Multiplication and Differentiation -- Convolution of Distributions -- The Laplacian on an Open Set. I. Function Spaces and Their Duals: The Space of Continous Functions on a Compact Set -- Locally Compact Spaces and Radon Measures -- Hilbert Spaces -- Lp Spaces II. Operators: Spectra -- Compact Operators III. Distributions: Definitions and Examples -- Multiplication and Differentiation -- Convolution of Distributions -- The Laplacian on an Open Set.