Partial differential equations: topics in Fourier analysis
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2014
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| Series: | A Chapman & Hall book
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. [169] - 171 |
| Physical Description: | VIII, 174 S. graph. Darst. |
| ISBN: | 9781466584013 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
1 The Multi-Index Notation 1
2 The Gamma Function 7
3 Convolutions 11
4 Fourier Transforms 21
5 Tempered Distributions 33
6 The Heat Kernel 43
7 The Free Propagator 53
8 The Newtonian Potential 63
9 The Bessel Potential 69
10 Global Hypoellipticity in the Schwartz Space 73
11 The Poisson Kernel 81
12 The Bessel—Poisson Kernel 87
13 Wave Kernels 93
14 The Heat Kernel of the Hermite Operator 103
15 The Green Function of the Hermite Operator 111
16 Global Regularity of the Hermite Operator 121
17 The Heisenberg Group 127
18 The Sub-Laplacian and the Twisted Laplacians 137
19 Convolutions on the Heisenberg Group 143
v
vi
20 Wigner Transforms and Weyl Transforms 147
21 Spectral Analysis of Twisted Laplacians 153
22 Heat Kernels Related to the Heisenberg Group 159
23 Green Functions Related to the Heisenberg Group 165
Bibliography 169
Index 173
Mathematics
Partial Differential Equations
Partial Differential Equations: Topics in Fourier Analysis explains
how to use the Fourier transform and heuristic methods to obtain
significant insight into the solutions of standard PDE models. It shows
how this powerful approach is valuable in getting plausible answers
that can then be justified by modern analysis.
Using Fourier analysis, the text constructs explicit formulas for solving
PDEs governed by canonical operators related to the Laplacian on the
Euclidean space. It focuses on the Laplacian, the Hermite operator,
the sub-Laplacian, and twisted Laplacians.
Features
• Provides explicit formulas for the solutions of PDEs important in
physics
• Solves the equations using methods based on Fourier analysis
• Presents the equations in order of complexity
• Covers the necessary background, including the gamma
function, convolutions, and distribution theory
• Incorporates historical notes on significant mathematicians and
physicists, showing you how mathematical contributions are the
culmination of many individual efforts
Through its coverage of fundamental examples of PDEs, this book
prepares you for studying more advanced topics such as pseudo-
differential operators. It also helps you appreciate PDEs as beautiful
structures in analysis, rather than a bunch of isolated ad-hoc
techniques.
ISBN: ^7ö-l-4LbS-ßMDl-3
|
| any_adam_object | 1 |
| author | Wong, Man Wah 1951- |
| author_GND | (DE-588)1013960645 |
| author_facet | Wong, Man Wah 1951- |
| author_role | aut |
| author_sort | Wong, Man Wah 1951- |
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| building | Verbundindex |
| bvnumber | BV041349975 |
| classification_rvk | SK 450 SK 540 |
| ctrlnum | (OCoLC)862812190 (DE-599)OBVAC10898075 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041349975 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:54:39Z |
| institution | BVB |
| isbn | 9781466584013 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026798570 |
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| physical | VIII, 174 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | CRC Press |
| record_format | marc |
| series2 | A Chapman & Hall book |
| spelling | Wong, Man Wah 1951- Verfasser (DE-588)1013960645 aut Partial differential equations topics in Fourier analysis M. W. Wong Boca Raton, Fla. [u.a.] CRC Press 2014 VIII, 174 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Literaturverz. S. [169] - 171 Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Erscheint auch als Online-Ausgabe 978-1-466-58407-5 Erscheint auch als Online-Ausgabe, PDF 978-1-466-58403-7 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026798570&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026798570&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Wong, Man Wah 1951- Partial differential equations topics in Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4044779-0 |
| title | Partial differential equations topics in Fourier analysis |
| title_auth | Partial differential equations topics in Fourier analysis |
| title_exact_search | Partial differential equations topics in Fourier analysis |
| title_full | Partial differential equations topics in Fourier analysis M. W. Wong |
| title_fullStr | Partial differential equations topics in Fourier analysis M. W. Wong |
| title_full_unstemmed | Partial differential equations topics in Fourier analysis M. W. Wong |
| title_short | Partial differential equations |
| title_sort | partial differential equations topics in fourier analysis |
| title_sub | topics in Fourier analysis |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Harmonische Analyse Partielle Differentialgleichung |
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