Analysis of spherical symmetries in Euclidean spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY ; Berlin [u.a.]
Springer
1998
|
| Series: | Applied Mathematical Sciences
129 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 223 Seiten |
| ISBN: | 0387949496 |
Staff View
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| 245 | 1 | 0 | |a Analysis of spherical symmetries in Euclidean spaces |c Claus Müller |
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Record in the Search Index
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| adam_text | Contents
Preface v
Introduction 1
§1 Notations and Basic Theorems 1
1 The General Theory 9
§2 Primitive Spaces 10
§3 The Completeness 23
§4 The Punk Hecke Formula 29
§5 Representations and Interpolations 31
§6 Homogeneous Harmonics 33
2 The Specific Theories 37
§7 The Legendre Polynomials 37
§8 The Laplace Integrals 41
§9 The Gegenbauer Polynomials 44
§10 The Associated Legendre Functions 51
§11 The Associated Spaces y^(q) 55
§12 Harmonic Differential Operators 61
§13 Maxwell s Theory of Multipoles 67
3 Spherical Harmonics and Differential Equations 75
§14 The Laplace Beltrami Operators 75
§15 Spherical Harmonics as Eigenfunctions 81
viii Introduction
§16 The Legendre Differential Equation 85
§17 The Legendre Functions as Hypergeometric Functions ... 91
4 Analysis on the Complex Unit Spheres 95
§18 Homogeneous Harmonics in C9 96
§19 Invariant Integrals on S* 1 100
§20 Complexification of the Funk Hecke Formula 108
§21 An Alternative System of Legendre Functions 112
5 The Bessel Functions 119
§22 Regular Bessel Functions 120
§23 Regular Hankel Functions 124
§24 Recursive and Asymptotic Relations 127
§25 Addition Formulas for Hankel Functions of Order Zero . . . 138
§26 Exponential Integrals with Bessel Functions 143
§27 The Traditional Notations 147
6 Integral Transforms 151
§28 Fourier Integrals 152
§29 The Fourier Representation Theorem 154
§30 The Parseval Identity 159
§31 Examples 163
7 The Radon Transform 173
§32 Radon Transforms and Fourier Transforms 173
§33 Radon Transforms and Spherical Symmetries 178
§34 The Nicholson Formulas 186
8 Appendix 195
§35 The T Function 195
§36 The Hypergeometric Function 203
§37 Elementary Asymptotics 207
References 213
Index 217
|
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| indexdate | 2024-07-09T18:14:48Z |
| institution | BVB |
| isbn | 0387949496 |
| language | English |
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| physical | VIII, 223 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Müller, Claus 1920-2008 Verfasser (DE-588)117727628 aut Analysis of spherical symmetries in Euclidean spaces Claus Müller New York, NY ; Berlin [u.a.] Springer 1998 VIII, 223 Seiten txt rdacontent n rdamedia nc rdacarrier Applied Mathematical Sciences 129 Mathematische Physik Mathematical physics Spherical harmonics Kugelfunktion (DE-588)4033494-6 gnd rswk-swf Euklidischer Raum (DE-588)4309127-1 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Kugelsymmetrie (DE-588)4202374-9 gnd rswk-swf Euklidischer Raum (DE-588)4309127-1 s Kugelsymmetrie (DE-588)4202374-9 s Spezielle Funktion (DE-588)4182213-4 s DE-604 Kugelfunktion (DE-588)4033494-6 s Applied Mathematical Sciences 129 (DE-604)BV000005274 129 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007912667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Müller, Claus 1920-2008 Analysis of spherical symmetries in Euclidean spaces Applied Mathematical Sciences Mathematische Physik Mathematical physics Spherical harmonics Kugelfunktion (DE-588)4033494-6 gnd Euklidischer Raum (DE-588)4309127-1 gnd Spezielle Funktion (DE-588)4182213-4 gnd Kugelsymmetrie (DE-588)4202374-9 gnd |
| subject_GND | (DE-588)4033494-6 (DE-588)4309127-1 (DE-588)4182213-4 (DE-588)4202374-9 |
| title | Analysis of spherical symmetries in Euclidean spaces |
| title_auth | Analysis of spherical symmetries in Euclidean spaces |
| title_exact_search | Analysis of spherical symmetries in Euclidean spaces |
| title_full | Analysis of spherical symmetries in Euclidean spaces Claus Müller |
| title_fullStr | Analysis of spherical symmetries in Euclidean spaces Claus Müller |
| title_full_unstemmed | Analysis of spherical symmetries in Euclidean spaces Claus Müller |
| title_short | Analysis of spherical symmetries in Euclidean spaces |
| title_sort | analysis of spherical symmetries in euclidean spaces |
| topic | Mathematische Physik Mathematical physics Spherical harmonics Kugelfunktion (DE-588)4033494-6 gnd Euklidischer Raum (DE-588)4309127-1 gnd Spezielle Funktion (DE-588)4182213-4 gnd Kugelsymmetrie (DE-588)4202374-9 gnd |
| topic_facet | Mathematische Physik Mathematical physics Spherical harmonics Kugelfunktion Euklidischer Raum Spezielle Funktion Kugelsymmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007912667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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