Fractal Functions, Fractal Surfaces, and Wavelets is the first systematic exposition of the theory of fractal surfaces, a natural outgrowth of fractal sets and fractal functions. It is also the first treatment to bring these general considerations to bear on the burgeoning field of wavelets. The text is based on Massopusts work on and contributions to the theory of fractal functions, and the author uses a number of tools--including analysis, topology, algebra, and probability theory--to introduce readers to this new subject. Though much of the material presented in this book is relatively current (developed in the past decade by the author and his colleagues) and fairly specialized, an informative background is provided for those
* First systematic treatment of fractal surfaces
* Links fractals and wavelets
* Provides background for those entering the field
* Contains color insert
Author(s): Peter R. Massopust (Auth.)
Publisher: Elsevier Inc
Year: 1994
Language: English
Pages: 379
Tags: Приборостроение;Обработка сигналов;Вейвлет-анализ;
Content:
Front Matter, Page iii
Copyright, Page iv
Preface, Pages ix-xi
Chapter 1 - Mathematical Preliminaries, Pages 3-39
Chapter 2 - Construction of Fractal Sets, Pages 41-86
Chapter 3 - Dimension Theory, Pages 87-116
Chapter 4 - Dynamical Systems and Dimension, Pages 117-131
Chapter 5 - Fractal Function Construction, Pages 135-203
Chapter 6 - Dimension of Fractal Functions, Pages 205-233
Chapter 7 - Fractal Functions and Wavelets, Pages 235-304
Chapter 8 - Fractal Surfaces, Pages 305-312,312a,312b,313-343
Chapter 9 - Fractal Wavelets in ℝn, Pages 345-357
List of Symbols, Pages 359-361
Bibliography, Pages 363-376
Index, Pages 377-383