Fractal Functions, Fractal Surfaces, and Wavelets

Hardcover | January 4, 1995

byPeter R. MassopustEditorPeter R. Massopust

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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

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From Our Editors

The first systematic exposition of the theory of fractal surfaces--based on the author's work on and contributions to the theory of fractal functions. Though much of the material presented here is relatively current (developed in the past decade by the author and his colleagues) and fairly specialized, an informative background is prov...

From the Publisher

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 ...

From the Jacket

Fractal surfaces are a natural outgrowth of fractal sets and fractal functions. Fractal Functions, Fractal Surfaces, and Wavelets provides the first systematic exposition of the theory and applications of fractal surfaces and their increasing significance in the burgeoning field of wavelets.Massopust's extensive work on and contributio...

Peter R. Massopust is a Privatdozent in the Center of Mathematics at the Technical University of Munich, Germany. He received his Ph.D. in Mathematics from the Georgia Institute of Technology in Atlanta, Georgia, USA, and his habilitation from the Technical University of Munich. He worked at several universities in the United States, a...

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Format:HardcoverDimensions:383 pages, 9 × 6 × 0.98 inPublished:January 4, 1995Publisher:Academic PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0124788408

ISBN - 13:9780124788404

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Table of Contents

(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 ClassCk.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 inR n+M. Properties of Fractal Surfaces. Fractal Surfaces of ClassCk.Fractal Surfaces and Wavelets in R n: Brief Review of Coxeter Groups. Fractal Functions on Foldable Figures. Interpolation on Foldable Figures. Dilation andWInvariant Spaces. Multiresolution Analyses. List of Symbols. Bibliography. Author Index. Subject Index.

From Our Editors

The first systematic exposition of the theory of fractal surfaces--based on the author's work on and contributions to the theory of fractal functions. Though much of the material presented here is relatively current (developed in the past decade by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. Full-color illus.

Editorial 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