Fractal Functions, Fractal Surfaces, and Wavelets
Autor Peter R. Massopusten Limba Engleză Hardback – 5 feb 1995
- First systematic treatment of fractal surfaces
- Links fractals and wavelets
- Provides background for those entering the field
- Contains color insert
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Specificații
ISBN-13: 9780124788404
ISBN-10: 0124788408
Pagini: 383
Dimensiuni: 152 x 229 x 24 mm
Greutate: 0.69 kg
Editura: ELSEVIER SCIENCE
ISBN-10: 0124788408
Pagini: 383
Dimensiuni: 152 x 229 x 24 mm
Greutate: 0.69 kg
Editura: ELSEVIER SCIENCE
Public țintă
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.Cuprins
(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.
Recenzii
"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