To order this title, and for more information, click here
By Peter Massopust, Sam Houston State University
Description 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
Audience
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.
Contents (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
R n+M. Properties of Fractal Surfaces. Fractal Surfaces
of Class Ck.
Fractal Surfaces and Wavelets in R 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.
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
Home | Elsevier Sites | Privacy Policy | Terms and Conditions | Feedback | Site Map | A Reed Elsevier Company