Abstract

(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 C gt gt . Dimension of Fractal Functions: gt Dimension Calculations. Function Spaces and Dimension. Fractal Functions and Wavelets: gt Basic Wavelet Theory. Fractal Function Wavelets. Fractal Surfaces: gt Tensor Product Fractal Surfaces. Affine Fractal Surfaces in R gt n+M gt . Properties of Fractal Surfaces. Fractal Surfaces of Class Ck gt . Fractal Surfaces and Wavelets in R gt n gt : gt Brief Review of Coxeter Groups. Fractal Functions on Foldable Figures. Interpolation on Foldable Figures. Dilation and W gt Invariant Spaces. Multiresolution Analyses. List of Symbols. Bibliography. Author Index. Subject Index.

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