Fractal Functions, Fractal Surfaces, and Wavelets

By: Peter R. Massopust

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Hardcover | 4 January 1995

At a Glance

Hardcover
383 Pages

Dimensions(cm)
23.7 x 15.93 x 2.36

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Published: 12th August 2016

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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

Industry Reviews

"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." --D.E. Bentil,University of Massachusetts at Amherst

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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
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 R n+M
Properties of Fractal Surfaces
Fractal Surfaces of Class Ck
Fractal Surfaces and Wavelets in R n : 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
Table of Contents provided by Publisher. All Rights Reserved.

Fractal Functions, Fractal Surfaces, and Wavelets

At a Glance

New Edition

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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