Fractal Functions, Fractal Surfaces, and WaveletsBy
- Peter Massopust
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
Mathematicians interested in a coherent and general presentation of the theory of fractal functions, surfaces, and wavelets; applied scientists in the fields of physics and computer science; libraries. Also suitable as a text for a seminar or workshop concentrating on different aspects of classical analysis.
Hardbound, 383 Pages
Published: January 1995
Imprint: Academic Press
"Massopust provides the basic theory and results from manipulating fractal functions and surfaces, and discusses future directions and applications to wavelet theory and fractal dynamics...Recommended."
- (Subchapter Titles): I. Foundations. Mathematical Preliminaries: Analysis and Topology. Probability Theory. Algebra. Construction of Fractal Sets: Classical Fractal Sets. Iterated Function Systems. Recurrent Sets. Graph Directed Fractal Constructions. Dimension Theory: Topological Dimensions. Metric Dimensions. Probabilistic Dimensions. Dimension Results for Self-Affine Fractals. The Box Dimension of Projections. Dynamical Systems and Dimension. II. Fractal Functions and Fractal Surfaces: Fractal Function Construction: The Read-BajraktarevicOperator. Recurrent Sets as Fractal Functions. Iterative Interpolation Functions. Recurrent Fractal Functions. Hidden Variable Fractal Functions. Properties of Fractal Functions. Peano Curves. Fractal Functions of Class Ck. Dimension of Fractal Functions: Dimension Calculations. Function Spaces and Dimension. Fractal Functions and Wavelets: Basic Wavelet Theory. Fractal Function Wavelets. Fractal Surfaces: Tensor Product Fractal Surfaces. Affine Fractal Surfaces in Rn+M. Properties of Fractal Surfaces. Fractal Surfaces of Class Ck. Fractal Surfaces and Wavelets in Rn: Brief Review of Coxeter Groups. Fractal Functions on Foldable Figures. Interpolation on Foldable Figures. Dilation and W Invariant Spaces. Multiresolution Analyses. List of Symbols. Bibliography. Author Index. Subject Index.