
Fractal Functions, Fractal Surfaces, and Wavelets
Description
Key Features
- Offers a comprehensive presentation of fractal functions and fractal surfaces
- Includes latest developments in fractal interpolation
- Connects fractal geometry with wavelet theory
- Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets
- Deepens and extends the pedagogical content
Readership
Mathematicians working or beginning to work in the broad field of fractal geometry; physicists and engineers researching or employing fractal models; biomathematicians and computer scientists modelling fractal phenomena
Table of Contents
- Dedication
- About the author
- Preface to first edition
- Preface to second edition
- List of symbols
- Part I: Foundations
- 1: Mathematical preliminaries
- Abstract
- 1 Analysis and topology
- 2 Measures and probability theory
- 3 Algebra
- 4 Function spaces
- 2: Construction of fractal sets
- Abstract
- 1 Classical fractal sets
- 2 Iterated function systems
- 3 Local iterated function systems
- 4 Recurrent sets
- 5 Graph-directed fractal constructions
- 6 Transformations between fractal sets
- 3: Dimension theory
- Abstract
- 1 Topological dimensions
- 2 Metric dimensions
- 3 Probabilistic dimensions
- 4 Dimension results for self-affine fractal sets
- 5 The box dimension of projections
- 4: Dynamical systems and dimension
- Abstract
- 1 Ergodic theorems and entropy
- 2 Lyapunov dimension
- 1: Mathematical preliminaries
- Part II: Fractal Functions and Fractal Surfaces
- 5: Construction of fractal functions
- Abstract
- 1 The Read-Bajraktarević operator
- 2 Local fractal functions
- 3 Fractal bases for fractal functions
- 4 Recurrent sets as fractal functions
- 5 Iterative interpolation functions
- 6 Recurrent fractal functions
- 7 Hidden-variable fractal functions
- 8 Properties of fractal functions
- 9 Peano curves
- 10 Fractal functions of class Ck
- 11 Biaffine fractal functions
- 12 Local fractal functions and smoothness spaces
- 6: Fractels and self-referential functions
- Abstract
- 1 Fractels: definition and properties
- 2 A fractel Read-Bajraktarević operator
- 3 Further properties of fractels
- 7: Dimension of fractal functions
- Abstract
- 1 Affine fractal functions
- 2 Recurrent fractal functions
- 3 Hidden-variable fractal functions
- 4 Biaffine fractal functions
- 8: Fractal functions and wavelets
- Abstract
- 1 Basic wavelet theory
- 2 Fractal function wavelets
- 3 Orthogonal fractal function wavelets
- 4 Wavelets are piecewise fractal functions
- 9: Fractal surfaces
- Abstract
- 1 Tensor product fractal surfaces
- 2 Affine fractal surfaces in
- 3 Properties of fractal surfaces
- 4 Fractal surfaces of class Ck
- 10: Fractal surfaces and wavelets in ℝn
- Abstract
- 1 Fractal functions on foldable figures
- 2 Interpolation on foldable figures
- 3 Dilation- and
-invariant function spaces
- 4 Multiresolution analyses
- 5 Wavelet sets and fractal surfaces
- 5: Construction of fractal functions
- Bibliography
- Index
Product details
- No. of pages: 426
- Language: English
- Copyright: © Academic Press 2016
- Published: August 9, 2016
- Imprint: Academic Press
- Hardcover ISBN: 9780128044087
- eBook ISBN: 9780128044704
About the Author
Peter Massopust
Affiliations and Expertise
Ratings and Reviews
Latest reviews
(Total rating for all reviews)
Paulo A. Mon Mar 12 2018
The title is clear and direct about the reader will find in the text. As a math book, with a wide and broad scope on the fractal and multifractal topics.
In my opinion, this book is for anyone that want to deep reading about fractal in a exact mathmatics language with precise statement of theorems and mathmatics definitions that is quite hard to find in the same book. The text was written in very affordable math style.