Fractal Functions, Fractal Surfaces, and Wavelets (2^nd Ed.)

Langue : Anglais

Auteur : Massopust Peter R.

Couverture de l’ouvrage Fractal Functions, Fractal Surfaces, and Wavelets

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Biographie
Commentaire

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

Mathematicians working or beginning to work in the broad field of fractal geometry; physicists and engineers researching or employing fractal models; biomathematicians and computer scientists modelling fractal phenomena.

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, at the Sandia National Laboratories in Albuquerque (USA), and as a senior research scientist in industry before returning to the academic environment. He has written more than sixty peer-reviewed articles in the mathematical areas of Fourier Analysis, Approximation Theory, Fractals, Splines, and Harmonic Analysis and more than 20 technical reports while working in the non-academic environment. He has authored or coauthored two textbooks and two monographs, and coedited two Contemporary Mathematics Volumes and several Special Issues for peer-reviewed journals. He is on the editorial board of several mathematics journals and has given more than one hundred invited presentations at national and international conferences, workshops, and seminars.

Offers a comprehensive presentation of fractal functions and fractal surfaces
Includes latest developments in fractal interpolation
Connects fractal geometry with wavelet theory
Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets
Deepens and extends the pedagogical content