Hilbert Space Methods in Signal Processing

by Kennedy, Rodney A.; Sadeghi, Parastoo

• ISBN13: 9781107010031
• ISBN10: 1107010039
• Format: Hardcover
• Copyright: 2013-04-15
• Publisher: Cambridge Univ Pr

Summary

This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.

Table of Contents

Hilbert spaces

Introduction

Spaces

Operators

Introduction to operators

Bounded operators

Compact operators

Integral operators

Applications

Signals and systems analysis on the 2-sphere

Signal concentration and joint spatio-spectral analysis

Convolution on 2-sphere

Reproducing kernel Hilbert spaces

Table of Contents provided by Publisher. All Rights Reserved.