Foundations of Functional Analysis

Foundations of Functional Analysis provides fundamental concepts about the theory, application and various methods involving functional analysis for students, teachers, scientists and engineers. Divided into three parts it covers: ̈ Basic facts of linear algebra and real analysis ̈ Normed spaces, contraction mappings, linear operators between normed spaces and fundamental results on these topics. ̈ Hilbert spaces and the representation of continuous linear function with applications. In this self-contained book, all the concepts, results and their consequences are motivated and illustrated by numerous examples in each chapter with carefully chosen exercises. Content: I: Basic Analysis: Analysis and Linear Algebra / Concepts in Metric Spaces / II: Banach Spaces: Normed Spaces / Contraction Mappings and Applications / Linear Operators in Normed Spaces / III: Hilbert Spaces: Inner Product Spaces / Representation of Linear Functional Fourier Analysis and Applications / Bibliography / Index The purpose of this chapter is to give a brief review of the basic concepts from the theory of real and complex analysis which will be needed in what follows.