Subanalytic sheaves and Sobolev spaces:
Gespeichert in:
| Hauptverfasser: | , , , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Société Mathématique de France
[2016]
|
| Schriftenreihe: | Astérisque
383 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XVI, 120 Seiten |
| ISBN: | 9782856298442 |
Internformat
MARC
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| 245 | 1 | 0 | |a Subanalytic sheaves and Sobolev spaces |c S. Guillermou, G. Lebeau, A. Parusiński, P. Schapira & J.-P. Schneiders |
| 264 | 1 | |a Paris |b Société Mathématique de France |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a XVI, 120 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Astérisque |v 383 | |
| 500 | |a Literaturangaben | ||
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| 700 | 1 | |a Lebeau, Gilles |d 1954- |0 (DE-588)121523136 |4 aut | |
| 700 | 1 | |a Parusiński, Adam |0 (DE-588)1123094047 |4 aut | |
| 700 | 1 | |a Schapira, Pierre |d 1943- |0 (DE-588)10785130X |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-029316020 | ||
Datensatz im Suchindex
| _version_ | 1804176815394127872 |
|---|---|
| adam_text | TABLE OF CONTENTS
Introduction
xiii
Stephane Guillermou Pierre Schapira — Construction of sheaves on the
subanalytic site .......................................................
Introduction ...........................................................
Acknowledgments ..................................................
1. Subanalytic topologies ..............................................
1.1. Linear coverings ...............................................
Notations and conventions ........................................
The site Msa .....................................................
The site Msai ....................................................
1.2. Regular coverings ..............................................
2. Sheaves on subanalytic topologies ...................................
2.1. Sheaves ........................................................
Usual notations ..................................................
Sheaves on M and Msa .............................................
Sheaves on M and Msai ............................................
Sheaves on Msa and Msai ..........................................
2.2. T-*acyclic sheaves .............................................
Cech complexes ...................................................
Acyclic sheaves ..................................................
2.3. The functor Pgal ...............................................
Direct sums in derived categories ................................
The functor RT(U; ·) .............................................
The functor Rpsal* ...............................................
2.4. Open sets with Lipschitz boundaries ............................
Normal cones and Lipschitz boundaries ............................
A vanishing theorem ..............................................
3. Operations on sheaves ...............................................
3.1. Tensor product and internal horn ...............................
3.2. Operations for closed embeddings ...............................
/֊regular open sets ..............................................
1
2
4
4
4
4
5
5
9
12
12
12
13
13
14
17
17
18
20
20
23
24
25
25
27
30
30
30
30
TABLE OF CONTENTS
Inverse and direct images by closed embeddings ................... 34
3.3. Operations for submersions ..................................... 36
Another subanalytic topology .......................................... 36
Inverse and direct images ............................................. 37
4. Construction of sheaves ............................................. 38
4.1. Sheaves on the subanalytic site ................................ 38
Temperate growth ...................................................... 38
A cutoff lemma on Msa ................................................. 39
Gevrey growth ......................................................... 39
4.2. Sheaves on the linear subanalytic site ......................... 40
Temperate growth of a given order ................................ 40
Gevrey growth of a given order ................................... 41
Rings of differential operators .................................. 42
4.3. A refined cutoff lemma ......................................... 43
4.4. A comparison result ............................................ 44
4.5. Sheaves on complex manifolds ................................... 46
Sheaves on complex manifolds ..................................... 46
Solutions of holonomie ^-modules ................................. 47
5. Filtrations .............................................................. 48
5.1. Derived categories of filtered objects ......................... 48
Complements on abelian categories ..................................... 48
Abelian tensor categories ............................................. 50
Derived categories of filtered objects ................................ 50
Complements on filtered objects ....................................... 51
5.2. Filtrations on 53
The filtered ring of differential operators ...................... 54
The L°°-filtration on ............................... 56
The L°°֊filtration on ............................... 56
^ sal ^
5.3. A functorial filtration on regular holonomie modules ........... 57
References ............................................................. 59
Gilles Lebeau — Sobolev spaces and Sobolev sheaves ....................... 61
1. Introduction ............................................................. 62
Acknowledgement .......................................................... 63
2. Notations and basic results on Sobolev spaces ............................ 63
3. The case of Lipschitz U .................................................. 65
The case s 0 ........................................................ 68
The case s 0 ........................................................ 70
4. The spaces Xt(U) and YS(U) .................................... 72
4.1. The spaces Xt{U) .................................................... 72
4.2. The spaces YS(U) .................................................... 79
5. The sheaf ${s ............................................................ 80
TABLE OF CONTENTS
vii
5.1. The sheaf fCs for s 0 ............................................. 81
5.2. The sheaf fCs on M2, with s 0 ..................................... 83
6. Appendix ................................................................. 86
6.1. Interpolation ....................................................... 86
6.2. The usual definition of Sobolev spaces ......................... 89
The case s 0 ........................................................ 90
The case s 0 ........................................................ 92
References .................................................................. 94
Adam Parusinski — Regular subanalytic covers .................................. 95
1. Proofs ................................................................... 96
1.1. Reduction to the case M = Mn......................................... 96
1.2. Regular projections ................................................. 97
1.3. Cylindrical decomposition ........................................... 97
1.4. The case of a regular projection .................................... 98
1.5. Proof of Theorem 0.2 ................................................ 98
1.6. L-regular sets ...................................................... 99
1.7. Proof of Theorem 0.3 ............................................... 100
1.8. Proof of Theorem 0.1 ............................................... 101
2. Remarks on the o-minimal case ........................................... 102
References ................................................................. 102
Pierre Schapira Jean-Pierre Schneiders — Derived categories of filtered
objects .................................................................... 103
1. Introduction ............................................................ 103
2. A review on quasi-abelian categories .................................... 104
Derived categories ................................................... 105
Left ¿֊structure ..................................................... 106
Derived functors ..................................................... 106
3. Filtered objects ........................................................ 107
Basic properties of Fa (^) ........................................... 108
The Rees functor ..................................................... Ill
4. Filtered modules in an abelian tensor category .......................... 113
Abelian tensor categories ............................................ 113
A-rings and A-modules ................................................ 115
Filtered rings and modules ........................................... 116
Example: modules over a filtered sheaf of rings ...................... 119
References ................................................................. 120
|
| any_adam_object | 1 |
| author | Guillermou, Stéphane Lebeau, Gilles 1954- Parusiński, Adam Schapira, Pierre 1943- Schneiders, Jean-Pierre |
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| ctrlnum | (OCoLC)964447595 (DE-599)OBVAC13390447 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-10T07:38:11Z |
| institution | BVB |
| isbn | 9782856298442 |
| language | English |
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| physical | XVI, 120 Seiten |
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| spelling | Subanalytic sheaves and Sobolev spaces S. Guillermou, G. Lebeau, A. Parusiński, P. Schapira & J.-P. Schneiders Paris Société Mathématique de France [2016] © 2016 XVI, 120 Seiten txt rdacontent n rdamedia nc rdacarrier Astérisque 383 Literaturangaben Zusammenfassungen in französischer und englischer Sprache Garbentheorie (DE-588)4155956-3 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Sobolev-Raum (DE-588)4055345-0 s Garbentheorie (DE-588)4155956-3 s DE-604 Guillermou, Stéphane (DE-588)1121044808 aut Lebeau, Gilles 1954- (DE-588)121523136 aut Parusiński, Adam (DE-588)1123094047 aut Schapira, Pierre 1943- (DE-588)10785130X aut Schneiders, Jean-Pierre (DE-588)1123094667 aut Astérisque 383 (DE-604)BV002579439 383 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029316020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Guillermou, Stéphane Lebeau, Gilles 1954- Parusiński, Adam Schapira, Pierre 1943- Schneiders, Jean-Pierre Subanalytic sheaves and Sobolev spaces Astérisque Garbentheorie (DE-588)4155956-3 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4155956-3 (DE-588)4055345-0 (DE-588)4143413-4 |
| title | Subanalytic sheaves and Sobolev spaces |
| title_auth | Subanalytic sheaves and Sobolev spaces |
| title_exact_search | Subanalytic sheaves and Sobolev spaces |
| title_full | Subanalytic sheaves and Sobolev spaces S. Guillermou, G. Lebeau, A. Parusiński, P. Schapira & J.-P. Schneiders |
| title_fullStr | Subanalytic sheaves and Sobolev spaces S. Guillermou, G. Lebeau, A. Parusiński, P. Schapira & J.-P. Schneiders |
| title_full_unstemmed | Subanalytic sheaves and Sobolev spaces S. Guillermou, G. Lebeau, A. Parusiński, P. Schapira & J.-P. Schneiders |
| title_short | Subanalytic sheaves and Sobolev spaces |
| title_sort | subanalytic sheaves and sobolev spaces |
| topic | Garbentheorie (DE-588)4155956-3 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Garbentheorie Sobolev-Raum Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029316020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
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