The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeat
Preface v Chapter 0. Introduction 1 x0.1. Linear partial di erential equations 1 Chapter 1. A rst look at Banach and Hilbert spaces 5 x1.1. Warm up: Metric and topological spaces 5 x1.2. The Banach space of continuous functions 14 x1.3. The geometry
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values o
Preface This book reflects the conclusions of the author to some simple questions: “What should an easy comprehensible introduction to classical mathematical analysis look like? Can we avoid the basic results on differential and integral calculus to
This text is designed both for students of probability and stochastic processes and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However
