Verfügbarkeit: Fractal functions, fractal surfaces, and wavelets

Fractal functions, fractal surfaces, and wavelets:

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Bibliographische Detailangaben
Beteilige Person:	Massopust, Peter Robert 1958- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	San Diego [u.a.] Acad. Press 1994
Schlagwörter:	Fraktal Funktion > Mathematik Oberfläche
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006850861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XI, 383 S. graph. Darst.
ISBN:	0124788408

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface ix I Foundations 1 1 Mathematical Preliminaries 3 1.1 Analysis and Topology ...................... 3 1.2 Probability Theory ........................ 18 1.3 Algebra .............................. 27 2 Construction of Fractal Sets 41 2.1 Classical Fractal Sets ....................... 42 2.1.1 Hausdorff measures and Hausdorff dimension ...... 43 2.1.2 Weierstraß-like fractal functions ............. 46 2.2 Iterated Function Systems .................... 47 2.2.1 Definition and properties of iterated function systems . 47 2.2.2 Moment theory and iterated function systems ..... 57 2.2.3 Recurrent iterated function systems ........... 59 2.2.4 Iterated Riemann surfaces ................ 64 2.3 Recurrent Sets ........................... 67 2.3.1 The construction of recurrent sets ............ 68 2.3.2 Subshifts of finite type and the connection to recurrent IFSs ....................... 76 2.4 Graph Directed Fractal Constructions .............. 84 3 Dimension Theory 87 3.1 Topological Dimensions ...................... 87 3.2 Metric Dimensions ........................ 92 3.3 Probabilistic Dimensions ..................... 99 3.4 Dimension Results for Self-Affine Fractals ........... 102 3.4.1 Dimension of self-similar fractals ............ 103 3.4.2 Dimension of self-affine fractals ............. 106 3.4.3 Recurrent IFSs and dimension .............. 108 3.4.4 Recurrent sets and Mauldin-Williams fractals ..... 110 3.5 The Box Dimension of Projections ................ Ill Dynamical Systems and Dimension 117 II Fractal Functions and Fractal Surfaces 133 5 Fractal Function Construction 135 5.1 The Read-Bajraktarević Operator ................ 135 5.2 Recurrent Sets as Fractal Functions ............... 146 5.3 Iterative Interpolation Functions ................. 149 5.4 Recurrent Fractal Functions ................... 160 5.5 Hidden Variable Fractal Functions ................ 162 5.6 Properties of Fractal Functions ................. 168 5.6.1 Moment theory of fractal functions ........... 168 5.6.2 Integral transforms of fractal functions ......... 173 5.6.3 Fractal functions and Dirichlet splines ......... 175 5.6.4 Lipschitz continuity of fractal functions ......... 181 5.6.5 Extrema of fractal functions ............... 182 5.7 Peano Curves ........................... 187 5.8 Fractal Functions of Class Ck .................. 195 6 Dimension of Fractal Functions 205 6.1 Dimension Calculations ...................... 205 6.1.1 Affine fractal functions .................. 205 6.1.2 Recurrent fractal functions ................ 211 6.1.3 Hidden variable fractal functions ............ 214 6.2 Function Spaces and Dimension ................. 218 6.2.1 Some basic function space theory ............ 219 6.2.2 Box dimension and smoothness ............. 229 7 Fractal Functions and Wavelets 235 7.1 Basic Wavelet Theory ....................... 236 7.2 Fractal Function Wavelets .................... 258 7.2.1 The general construction ................. 259 7.2.2 A multiresolution analysis of Cb(lR) ........... 274 7.3 Orthogonal Fractal Function Wavelets ............. 277 7.4 iV-refinable Scaling Functions .................. 300 8 Fractal Surfaces 305 8.1 Tensor Product Fractal Surfaces ................. 306 8.2 Affine Fractal Surfaces in H * 1 ................. 308 8.2.1 The construction ..................... 309 8.2.2 IR-valued affine fractal surfaces ............. 310 8.3 Properties of Fractal Surfaces .................. 316 8.3.1 The oscillation of ƒ* ................... 316 8.3.2 Box dimension of the projections ƒ ........... 322 8.3.3 Box dimension of ƒ Є RF(X С IR2, IR) ........ 328 8.3.4 Holder continuity ..................... 333 8.3.5 p-balanced measures and moment theory for ƒ** .... 334 8.4 Fractal Surfaces of Class Ck ................... 337 8.4.1 Construction via IFSs .................. 337 8.4.2 Smooth fractal surfaces via integration ......... 340 9 Fractal Wavelets in ЇЇГ 345 9.1 Brief Review of Coxeter Groups ................. 345 9.2 Fractal Functions on Foldable Figures .............. 349 9.3 Interpolation on Foldable Figures ................ 351 9.4 Dilation and W Invariant Spaces ................ 353 9.5 Multiresolution Analyses ..................... 355 List of Symbols 359 Bibliography 363 Index 377
any_adam_object	1
author	Massopust, Peter Robert 1958-
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	514 - Topology
dewey-raw	514.74
dewey-search	514.74
dewey-sort	3514.74
dewey-tens	510 - Mathematics
discipline	Physik Mathematik
format	Book
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indexdate	2024-12-20T09:51:33Z
institution	BVB
isbn	0124788408
language	English
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physical	XI, 383 S. graph. Darst.
publishDate	1994
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publisher	Acad. Press
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spellingShingle	Massopust, Peter Robert 1958- Fractal functions, fractal surfaces, and wavelets Fraktal (DE-588)4123220-3 gnd Funktion Mathematik (DE-588)4071510-3 gnd Oberfläche (DE-588)4042907-6 gnd
subject_GND	(DE-588)4123220-3 (DE-588)4071510-3 (DE-588)4042907-6
title	Fractal functions, fractal surfaces, and wavelets
title_auth	Fractal functions, fractal surfaces, and wavelets
title_exact_search	Fractal functions, fractal surfaces, and wavelets
title_full	Fractal functions, fractal surfaces, and wavelets Peter R. Massopust
title_fullStr	Fractal functions, fractal surfaces, and wavelets Peter R. Massopust
title_full_unstemmed	Fractal functions, fractal surfaces, and wavelets Peter R. Massopust
title_short	Fractal functions, fractal surfaces, and wavelets
title_sort	fractal functions fractal surfaces and wavelets
topic	Fraktal (DE-588)4123220-3 gnd Funktion Mathematik (DE-588)4071510-3 gnd Oberfläche (DE-588)4042907-6 gnd
topic_facet	Fraktal Funktion Mathematik Oberfläche
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006850861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT massopustpeterrobert fractalfunctionsfractalsurfacesandwavelets

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