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Fractal Functions, Fractal Surfaces, and Wavelets
This updated and expanded second edition is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets
Peter R. Massopust (Author)
9780128044087
Hardback, published 9 August 2016
426 pages
22.9 x 15.1 x 2.7 cm, 0.86 kg
Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content.
Part I: Foundations1. Mathematical preliminaries2. Construction of fractal sets3. Dimension theory4. Dynamical systems and dimension Part II: Fractal Functions and Fractal Surfaces5. Construction of fractal functions6. Fractels and self-referential functions7. Dimension of fractal functions8. Fractal functions and wavelets9. Fractal surfaces10. Fractal surfaces and wavelets in Rn
Subject Areas: Differential & Riemannian geometry [PBMP]
