Fractal functions, fractal surfaces, and wavelets:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
San Diego [u.a.]
Acad. Press
1994
|
| Subjects: | |
| 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 |
| Physical Description: | XI, 383 S. graph. Darst. |
| ISBN: | 0124788408 |
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MARC
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| 245 | 1 | 0 | |a Fractal functions, fractal surfaces, and wavelets |c Peter R. Massopust |
| 264 | 1 | |a San Diego [u.a.] |b Acad. Press |c 1994 | |
| 300 | |a XI, 383 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
| DE-BY-TUM_call_number | 0001 96 A 456 0831 SK.162 |
|---|---|
| DE-BY-TUM_katkey | 739655 |
| DE-BY-TUM_location | Mag LSB |
| DE-BY-TUM_media_number | 040001569379 TEMP2918991 |
| _version_ | 1821931107329769472 |
| 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- |
| author_GND | (DE-588)140877789 |
| author_facet | Massopust, Peter Robert 1958- |
| author_role | aut |
| author_sort | Massopust, Peter Robert 1958- |
| author_variant | p r m pr prm |
| building | Verbundindex |
| bvnumber | BV010297062 |
| classification_rvk | SK 380 UG 3900 |
| classification_tum | MAT 519f |
| ctrlnum | (OCoLC)246763173 (DE-599)BVBBV010297062 |
| dewey-full | 514.74 |
| 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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| id | DE-604.BV010297062 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:51:33Z |
| institution | BVB |
| isbn | 0124788408 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006850861 |
| oclc_num | 246763173 |
| open_access_boolean | |
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| owner_facet | DE-29T DE-703 DE-739 DE-91 DE-BY-TUM DE-522 DE-83 DE-525 DE-188 |
| physical | XI, 383 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Acad. Press |
| record_format | marc |
| 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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