Wavelets
A Student Guide
Seiten
2017
Cambridge University Press (Verlag)
978-1-107-61251-8 (ISBN)
Cambridge University Press (Verlag)
978-1-107-61251-8 (ISBN)
The mathematical theory of wavelets is intrinsically advanced. However, the author's elementary approach makes this text an excellent introduction to the subject for senior undergraduate students. The theory is supplemented by more than 200 exercises so students can explore the fundamental ideas and numerous applications of wavelets.
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.
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.
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.
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.
| Erscheinungsdatum | 28.01.2017 |
|---|---|
| Reihe/Serie | Australian Mathematical Society Lecture Series |
| Zusatzinfo | Worked examples or Exercises; 20 Line drawings, black and white |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 151 x 228 mm |
| Gewicht | 410 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| ISBN-10 | 1-107-61251-9 / 1107612519 |
| ISBN-13 | 978-1-107-61251-8 / 9781107612518 |
| Zustand | Neuware |
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