Differential operators of infinite order with real arguments and their applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 240 S. graph. Darst. |
| ISBN: | 9810216114 |
Internformat
MARC
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| 245 | 1 | 0 | |a Differential operators of infinite order with real arguments and their applications |c Tran Duc Van ; Dinh Nho Hào |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1994 | |
| 300 | |a VII, 240 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Differential operators | |
| 650 | 0 | 7 | |a Differentialoperator |0 (DE-588)4012251-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialoperator |0 (DE-588)4012251-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Đinh, Nho-Hào |d 1961- |e Verfasser |0 (DE-588)112326129 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804127409244471296 |
|---|---|
| adam_text | CONTENTS
Introduction 1
Chapter 1. Preliminaries 9
1.1. Spaces Ck{n) and Lp(fl) 9
1.2. Definitions and basic properties of distributions 10
1.3. Multiplication of distributions by functions 11
1.4. Differentiation of distributions 11
1.5. Distributions with compact support 11
1.6. Convolution of distributions 12
1.7. Fourier transforms of distributions 13
1.8. The space of analytic functionals 14
1.9. Entire functions of exponential type that are bounded on IRn 16
1.10. Difference quotients and modulus of continuity 16
1.11. The sampling theorems 18
1.12. The de la Vallee Poussin kernel 18
1.13. The Dirichlet kernels 20
1.14. Markov type theorems 21
115. The second interpolation method of Bernstein 21
1.16. Orlicz classes and Orlicz spaces 22
1.17. Sobolev Orlicz spaces 24
1.18. The Denjoy Carleman classes and the quasianalyticity of
functions of several real variables 26
119. Semifinitary functions 28
1.20. Weakly nonlinear equations 28
Chapter 2. Pseudo differential operators with real analytic symbols ... 30
2.1. The space of test functions in a neighborhood of zero 32
2.2. Differential operators of infinite order (DOIO) 36
2.3. The space of generalized functions W^HT) 39
2.4. The algebra of pseudo differential operators with analytic symbols 45
Bibliographical Notes 47
v
vi CONTENTS
Chapter 3. Applications to pseudo differential equations 48
3.1. Problems in the whole Euclidean space 49
3.2. The Cauchy problem in the space
of functions valued in W^°°(IR ) 52
3.3. The Cauchy problem in the space VFg°°(IR )
and its fundamental solution 54
3.4. The Cauchy problem for ordinary pseudo differential equations 56
3.5. Boundary value problems 57
3.6. Multi dimensional integral equations of the first kind with
entire kernels 59
3.7. Functional equations 63
3.8. A class of real analytic symbols with weights 70
Bibliographical Notes 75
Chapter 4. Approximation methods 76
4.1. Approximating the symbols by algebraic polynomials 76
4.2. Approximating the symbols by trigonometric polynomials 79
4.3. Trigonometric interpolation 82
4.4. Approximating the data by sine functions 84
4.5. Examples 84
Bibliographical Notes 88
Chapter 5. A mollification method for ill posed problems 92
5.1. Introduction 92
5.2. Mollification method 93
5.3. Numerical differentiation 101
5.4. The heat equation backwards in time 105
5.5. The Cauchy problem for the Laplace equation 112
5.6. The non characteristic Cauchy problem for parabolic equations 114
5.7. Numerical case study 124
Bibliographical Notes 125
DIFFERENTIAL OPERATORS OF INFINITE ORDER vii
Chapter 6. Nontriviality of Sobolev Orlicz spaces of infinite order 128
6.1. Monotonic limits of Banach spaces 128
6.2. Nontriviality of Sobolev Orlicz spaces of infinite order in
a bounded domain 133
6.3. Nontriviality of Sobolev Orlicz spaces of infinite order on
the n dimensional torus 141
6.4. Nontriviality of Sobolev Orlicz spaces of infinite order
defined on a full Euclidean space 144
6.5. Nontriviality of Sobolev Orlicz spaces of infinite order in
angular domains 156
Bibliographical Notes 160
Chapter 7. Some properties of Sobolev Orlicz spaces
of infinite order 161
7.1. Traces and extensions 161
7.2. Traces in LW°°{$n, (0, a)} 163
7.3. Dual spaces 170
7.4. Imbedding theorems 174
Bibliographical Notes 194
Chapter 8. Elliptic equations of infinite order
with arbitrary nonlinearities 195
8.1. Elliptic boundary value problems 196
8.2. A model equation. Examples 204
8.3. Periodic problems. Inhomogeneous boundary problems 206
8.4. Degenerate nonlinear elliptic equations of infinite order 210
Bibliographical Notes 217
Bibliography 218
|
| any_adam_object | 1 |
| author | Tràn, Đúʾc-Văn Đinh, Nho-Hào 1961- |
| author_GND | (DE-588)112326161 (DE-588)112326129 |
| author_facet | Tràn, Đúʾc-Văn Đinh, Nho-Hào 1961- |
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| dewey-full | 515.7242 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7242 |
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| dewey-sort | 3515.7242 |
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| discipline | Mathematik |
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| id | DE-604.BV012741498 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:32:53Z |
| institution | BVB |
| isbn | 9810216114 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008664254 |
| oclc_num | 31184770 |
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| owner | DE-703 DE-11 DE-188 |
| owner_facet | DE-703 DE-11 DE-188 |
| physical | VII, 240 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Tràn, Đúʾc-Văn Verfasser (DE-588)112326161 aut Differential operators of infinite order with real arguments and their applications Tran Duc Van ; Dinh Nho Hào Singapore [u.a.] World Scientific 1994 VII, 240 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations Differential operators Differentialoperator (DE-588)4012251-7 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s DE-604 Đinh, Nho-Hào 1961- Verfasser (DE-588)112326129 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008664254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tràn, Đúʾc-Văn Đinh, Nho-Hào 1961- Differential operators of infinite order with real arguments and their applications Differential equations Differential operators Differentialoperator (DE-588)4012251-7 gnd |
| subject_GND | (DE-588)4012251-7 |
| title | Differential operators of infinite order with real arguments and their applications |
| title_auth | Differential operators of infinite order with real arguments and their applications |
| title_exact_search | Differential operators of infinite order with real arguments and their applications |
| title_full | Differential operators of infinite order with real arguments and their applications Tran Duc Van ; Dinh Nho Hào |
| title_fullStr | Differential operators of infinite order with real arguments and their applications Tran Duc Van ; Dinh Nho Hào |
| title_full_unstemmed | Differential operators of infinite order with real arguments and their applications Tran Duc Van ; Dinh Nho Hào |
| title_short | Differential operators of infinite order with real arguments and their applications |
| title_sort | differential operators of infinite order with real arguments and their applications |
| topic | Differential equations Differential operators Differentialoperator (DE-588)4012251-7 gnd |
| topic_facet | Differential equations Differential operators Differentialoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008664254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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