Synopses & Reviews
This book presents the fundamental function spaces and their duals, explores operator theory and finally develops the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Includes an assortment of well formulated exercises, with answers and hints collected at the end of the book.
Table of Contents
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.