Wavelets

A Student Guide

Peter Nickolas (University of Wollongong, New South Wales)

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English

Cambridge University Press
26 January 2017

Mathematics & Sciences; Functional analysis & transforms

Series: Australian Mathematical Society Lecture Series

This text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.

By: Peter Nickolas (University of Wollongong New South Wales)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 24
Dimensions: Height: 228mm, Width: 151mm, Spine: 15mm
Weight: 410g
ISBN: 9781107612518
ISBN 10: 1107612519
Series: Australian Mathematical Society Lecture Series
Pages: 274
Publication Date: 26 January 2017
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface; 1. An overview; 2. Vector spaces; 3. Inner product spaces; 4. Hilbert spaces; 5. The Haar wavelet; 6. Wavelets in general; 7. The Daubechies wavelets; 8. Wavelets in the Fourier domain; Appendix: notes on sources; References; Index.

Peter Nickolas is an Associate Professor in the School of Mathematics and Applied Statistics at the University of Wollongong, New South Wales. He has nearly 40 years of experience in teaching and research. A large part of his research has been in the theory of topological groups, but he has also made significant contributions to the emerging theory of free paratopological groups, to the study of the geometry of metric spaces and to applications of mathematics and formal logic in computer science.

Reviews for Wavelets: A Student Guide

'Not only does it bring the subject in a most suitable and systematic way that, I am sure, mathematics students are used to and probably appreciate most. It is also following some good rules of didactics taking the students by the hand and bringing them to a higher level of understanding, ensuring that at least the bulk of the students does not declutch. A lot of effort is put into taking the rungs of the ladder at just the right pace, not boringly slow or not frighteningly fast, and always placing a chapter in the proper context: what has been achieved, and where do we want to go?' Adhemar Bultheel, European Mathematical Society 'What is really nice with this book is its style, which leads the student step by step through different ideas, theorems and proofs. It explains the reason behind new concepts, discusses their shortcomings, and uses these as a motivation to introduce other concepts.' Salim Salem, MAA Reviews