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E-raamat: Fractal Functions, Fractal Surfaces, and Wavelets

(Centre of Mathematics, Technical University of Munich, Germany)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 28-Jun-2014
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780080924588
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Fractal Functions, Fractal Surfaces, and WaveletsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 28-Jun-2014
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780080924588
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A systematic exposition of the theory and application of fractal surfaces and their increasing significance in the field of wavelets. Employs such tools as analysis, topology, algebra, and probability theory, all of which the reader is assumed to have a graduate-level understanding. Annotation copyright Book News, Inc. Portland, Or.

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

Arvustused

"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

(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 CIV>
k. 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 RV>
n+M. Properties of Fractal Surfaces. Fractal Surfaces of Class CV>
k. Fractal Surfaces and Wavelets in RV>
n: 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.


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.
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