Wavelets

A Student Guide
Erscheinungsjahr 2017
ISBN: 978-1-107-61251-8
Verlag: Cambridge University Press

Buch, Englisch, Band 24, 280 Seiten, Format (B × H): 153 mm x 228 mm, Gewicht: 416 g

Reihe: 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.

Autoren/Hrsg.

Nickolas, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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.

Über Autor(innen)

Nickolas, Peter
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.