Constructive approximation on the sphere: with applications to geomathematics
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1998
|
| Series: | Numerical mathematics and scientific computation
Oxford science publications |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 427 S. Ill., graph. Darst. |
| ISBN: | 0198536828 9780198536826 |
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Record in the Search Index
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| adam_text | CONSTRUCTIVE APPROXIMATION ON THE SPHERE WITH APPLICATIONS TO
GEOMATHEMATICS W. FREEDEN GEOMATHEMATICS GROUP, UNIVERSITY OF
KAISERSLAUTERN T. GERVENS UNIVERSITY OFOSNABRIICK (FH) M. SCHREINER
GEOMATHEMATICS GROUP, UNIVERSITY OF KAISERSLAUTERN CLARENDON PRESS *
OXFORD 1998 CONTENTS LIST OF SYMBOLS XIII INTRODUCTION 1 1 NOTATION 7
1.1 BASIC SETTINGS 7 1.2 SPHERICAL NOMENCLATURE 8 SCALARS 2 POLYNOMIALS
21 2.1 HOMOGENEOUS POLYNOMIALS 21 2.2 HOMOGENEOUS HARMONIC POLYNOMIALS
25 2.3 ADDITION THEOREM 29 3 SCALAR SPHERICAL HARMONICS 35 3.1
DEFINITION 35 3.2 LEGENDRE POLYNOMIALS 38 3.3 FUNDAMENTAL SYSTEMS 46
3.4 CLOSURE AND COMPLETENESS 52 3.5 EIGENFUNCTIONS OF THE BELTRAMI
OPERATOR 59 3.6 FUNK-HECKE FORMULA 60 4 GREEN S FUNCTIONS 67 4.1
DEFINITION 67 4.2 INTEGRAL FORMULAE 72 4.3 BELTRAMI DIFFERENTIAL
EQUATION 78 5 SPHERICAL RADIAL BASIS FUNCTIONS 81 5.1 SOBOLEV SPACES AND
PSEUDODIFFERENTIAL OPERATORS 81 5.2 REPRODUCING KERNEL SOBOLEV SPACES 88
VIII CONTENTS 5.3 INTEGRAL FORMULAE 92 5.4 PEANO S THEOREM 97 5.5
LOCALIZATION 99 5.6 EXAMPLES OF RADIAL BASIS FUNCTIONS 105 5.6.1 GREEN S
KERNELS CORRESPONDING TO ITERATED BEL- TRAMI OPERATORS 105 5.6.2 KERNELS
CORRESPONDING TO INVERTIBLE PSEUDO- DIFFERENTIAL OPERATORS 107 5.6.3
ABEL-POISSON KERNEL AND RELATED FUNCTIONS 108 5.6.4 GAUFI-WEIERSTRAB
KERNEL AND RELATED FUNC- TIONS 112 5.7 POSITIVE DEFINITENESS 115 5.8
FURTHER EXAMPLES OF RADIAL BASIS FUNCTIONS 120 5.8.1 KERNELS RELATED TO
RADIAL BASIS FUNCTIONS OF EUCLIDEAN SPACES 120 5.8.2 LOCALLY SUPPORTED
KERNELS 123 5.9 STRICT POSITIVE DEFINITENESS 135 6 SPHERICAL SPLINES 139
6.1 VARIATIONAL CHARACTERIZATION OF SPLINE INTERPOLATION 139 6.1.1
SPHERICAL SPLINE INTERPOLATION, M = * 1 139 6.1.2 SPHERICAL SPLINE
INTERPOLATION, M 0 143 6.2 ERROR ESTIMATES 149 6.3 CONVERGENCE 153 6.4
COMPLETE SPLINE BASES 155 6.5 COMBINED INTERPOLATION AND SMOOTHING 157 7
APPROXIMATE INTEGRATION 165 7.1 LOW DISCREPANCY METHOD 166 7.2
INTERPOLATORY POLYNOMIAL INTEGRATION 177 7.3 BEST APPROXIMATIONS 185 7.4
INTERPOLATORY SPLINE INTEGRATION 188 8 SPHERICAL SINGULAR INTEGRALS 19 3
8.1 APPROXIMATE IDENTITIES 193 8.2 EXAMPLES OF SPHERICAL SINGULAR
INTEGRALS 197 8.2.1 ABEL-POISSON SINGULAR INTEGRAL 197 CONTENTS 8.2.2
GAUFI-WEIERSTRAFI SINGULAR INTEGRAL 199 8.2.3 _ _ SINGULAR INTEGRALS
CORRESPONDING TO LOCALLY SUPPORTED KERNEL FUNCTIONS 201 8.2.4 SPHERICAL
UP FUNCTION 207 9 GABOR AND TOEPLITZ TRANSFORMS 209 9.1 GABOR TRANSFORM
210 9.2 COMBINED FOURIER AND GABOR TRANSFORM 215 9.3 TOEPLITZ TRANSFORM
216 9.4 COMBINED FOURIER AND TOEPLITZ TRANSFORM 220 9.5 COMBINED GABOR
AND TOEPLITZ TRANSFORM 223 10 CONTINUOUS WAVELET TRANSFORM 227 10.1
CONTINUOUS WAVELET TRANSFORM (LINEAR THEORY) 229 10.2 CONTINUOUS WAVELET
TRANSFORM (BILINEAR THEORY) 234 10.2.1 RECONSTRUCTION FORMULA 234 10.2.2
SCALING FUNCTION 237 10.2.3 EXAMPLES 242 10.2.4 LEAST SQUARES PROPERTY
243 10.3 SCALE DISCRETIZED WAVELET TRANSFORM 246 10.3.1 P-SCALE
DISCRETIZED WAVELETS 246 10.3.2 M-SCALE DISCRETIZED WAVELETS. 252 10.3.3
MULTIRESOLUTION ANALYSIS BY MEANS OF SCALE DISCRETIZED WAVELETS. 255
10.3.4 -SCALE DISCRETIZED WAVELET TRANSFORM 262 10.3.5 LEAST SQUARES
PROPERTY 269 10.4 FULLY DISCRETIZED WAVELET TRANSFORM 270 10.5 COMBINED
SPHERICAL HARMONIC AND WAVELET EXPAN- SION 272 11 DISCRETE WAVELET
TRANSFORM 27 5 11.1 SCALE DISCRETE SCALING FUNCTION 276 11.1.1
ADMISSIBILITY CONDITION 276 11.1.2 SCALE DISCRETE SCALING FUNCTION 279
11.1.3 DISCRETE APPROXIMATE IDENTITY 280 11.2 SCALE DISCRETE
WAVELET-TRANSFORM 282 11.3 NON-BAND-LIMITED WAVELETS 287 11.3.1 RATIONAL
WAVELETS 287 11.3.2 MODIFIED RATIONAL WAVELET 288 X CONTENTS 11.3.3
EXPONENTIAL WAVELETS 289 11.4 BAND-LIMITED WAVELETS 290 11.4.1 SHANNON
WAVELETS 291 11.4.2 DE LA VALID POUSSIN WAVELETS 294 11.4.3 CUBIC
POLYNOMIAL WAVELETS 295 11.4.4 EXACT FULLY DISCRETE WAVELET TRANSFORM
296 11.4.5 A PYRAMID SCHEME 301 11.5 SCALE DISCRETE WAVELET TRANSFORM OF
POSITIVE ORDER 311 11.5.1 FIXED ORDER 312 11.5.2 INCREASING ORDER 315
VECTORS 12 VECTOR SPHERICAL HARMONICS 321 12.1 NOTATION 322 12.2
DEFINITION OF VECTOR SPHERICAL HARMONICS 323 12.3 HOMOGENEOUS HARMONIC
VECTOR POLYNOMIALS 324 12.4 DECOMPOSITION OF SPHERICAL VECTOR FIELDS 329
12.5 VECTORIAL BELTRAMI OPERATOR 331 12.6 VECTORIAL ADDITION THEOREM 333
12.7 VECTORIAL FUNK-HECKE FORMULAE 340 13 VECTORIAL APPROXIMATION
METHODS 345 13.1 SOBOLEV SPACES AND PSEUDODIFFERENTIAL OPERATORS 345
13.2 VECTORIAL SPLINES 348 13.3 VECTORIAL WAVELETS 350 13.4 SCALE
CONTINUOUS SPHERICAL WAVELETS 352 13.5 SCALE DISCRETE SPHERICAL WAVELETS
352 TENSORS 14 TENSOR SPHERICAL HARMONICS 357 14.1 NOTATION 358 14.2
DEFINITION OF TENSOR SPHERICAL HARMONICS 370 14.3 HOMOGENEOUS HARMONIC
TENSOR POLYNOMIALS 371 CONTENTS XI 14.4 DECOMPOSITION THEOREM 376 14.5
TENSORIAL BELTRAMI OPERATOR 380 14.6 TENSORIAL ADDITION THEOREM 383 14.7
TERISORIAL FUNK-HECKE FORMULA 392 15 TENSORIAL APPROXIMATION METHODS 399
REFERENCES 403 INDEX 421
|
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| discipline | Mathematik Geographie |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:18:10Z |
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| isbn | 0198536828 9780198536826 |
| language | English |
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| physical | XV, 427 S. Ill., graph. Darst. |
| publishDate | 1998 |
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| series2 | Numerical mathematics and scientific computation Oxford science publications |
| spelling | Freeden, Willi 1948- Verfasser (DE-588)121167259 aut Constructive approximation on the sphere with applications to geomathematics W. Freeden ; T. Gervens ; M. Schreiner Oxford Clarendon Press 1998 XV, 427 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerical mathematics and scientific computation Oxford science publications Hier auch später erschienene, unveränderte Nachdrucke Approximation, Théorie de l' ram Fonctions sphériques ram Sciences de la Terre - Mathématiques ram Mathematik Approximation theory Earth sciences Mathematics Spherical functions Sphärische Geometrie (DE-588)4182228-6 gnd rswk-swf Geodäsie (DE-588)4020202-1 gnd rswk-swf Sphärische Geometrie (DE-588)4182228-6 s Geodäsie (DE-588)4020202-1 s DE-604 Gervens, Theo Verfasser aut Schreiner, Michael Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008038829&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Freeden, Willi 1948- Gervens, Theo Schreiner, Michael Constructive approximation on the sphere with applications to geomathematics Approximation, Théorie de l' ram Fonctions sphériques ram Sciences de la Terre - Mathématiques ram Mathematik Approximation theory Earth sciences Mathematics Spherical functions Sphärische Geometrie (DE-588)4182228-6 gnd Geodäsie (DE-588)4020202-1 gnd |
| subject_GND | (DE-588)4182228-6 (DE-588)4020202-1 |
| title | Constructive approximation on the sphere with applications to geomathematics |
| title_auth | Constructive approximation on the sphere with applications to geomathematics |
| title_exact_search | Constructive approximation on the sphere with applications to geomathematics |
| title_full | Constructive approximation on the sphere with applications to geomathematics W. Freeden ; T. Gervens ; M. Schreiner |
| title_fullStr | Constructive approximation on the sphere with applications to geomathematics W. Freeden ; T. Gervens ; M. Schreiner |
| title_full_unstemmed | Constructive approximation on the sphere with applications to geomathematics W. Freeden ; T. Gervens ; M. Schreiner |
| title_short | Constructive approximation on the sphere |
| title_sort | constructive approximation on the sphere with applications to geomathematics |
| title_sub | with applications to geomathematics |
| topic | Approximation, Théorie de l' ram Fonctions sphériques ram Sciences de la Terre - Mathématiques ram Mathematik Approximation theory Earth sciences Mathematics Spherical functions Sphärische Geometrie (DE-588)4182228-6 gnd Geodäsie (DE-588)4020202-1 gnd |
| topic_facet | Approximation, Théorie de l' Fonctions sphériques Sciences de la Terre - Mathématiques Mathematik Approximation theory Earth sciences Mathematics Spherical functions Sphärische Geometrie Geodäsie |
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