Projections in several complex variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Soc. Math. de France
2010
|
| Schriftenreihe: | Mémoires de la SMF
123 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 8, 131 S. |
| ISBN: | 9782856293041 |
Internformat
MARC
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| 100 | 1 | |a Hsiao, Chin-Yu |e Verfasser |0 (DE-588)143531123 |4 aut | |
| 245 | 1 | 0 | |a Projections in several complex variables |c Chin-Yu Hsiao |
| 264 | 1 | |a Paris |b Soc. Math. de France |c 2010 | |
| 300 | |a 8, 131 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 650 | 0 | 7 | |a Cauchy-Riemannsche Mannigfaltigkeit |0 (DE-588)4147400-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1813056775930249216 |
|---|---|
| adam_text |
CONTENTS
Introduction
. 7
Acknowledgements
. 8
Part I. On the singularities of the
Szegő
projection for
(0,
q) forms
. 1
1.
Introduction and statement
of the main results
. 3
2.
ôb-Complex
and the
hypoellipicity of
Db, a
review
. 13
3.
The characteristic equation
. 19
4.
The heat equation, formal construction
. 25
5.
Some symbol classes
. 33
6.
The heat equation
. 45
7.
The
Szegő
Projection
. 57
8.
The leading term of the
Szegő
Projection
. 71
Part II. On the singularities of the Bergman projection for
(0,
q) forms
79
1.
Introduction and statement
of the main results
. 81
2.
The d-Neumann problem, a review
. 91
3.
The operator
Τ
. 95
4.
The principal symbols of
7Ö?rand
ηα^ρ'
. 99
5.
The operator
tìf
.103
6.
The heat equation for dL?)
.107
CONTENTS
7.
The Bergman projection
.119
Bibliography
.129
This work consists two parts. In the first part, we completely study the
heat equation method of Menikoff-Sj
östrand
and apply it to the Kohn
Laplacian defined on a compact
orientable
connected CR manifold. We
then get the full asymptotic expansion of the
Szegő
projection for
(0,
q)
forms when the
Levi
form is non-degenerate. This generalizes a result
of Boutet
de Monvel
and
Sjöstrand
for
(0,0)
forms. Our main tools
are Fourier integral operators with complex valued phase
Melin
and
Sjöstrand
functions.
In the second part, we obtain the full asymptotic expansion of
the Bergman projection for
(0,
q) forms when the
Levi
form is non-
degenerate. This also generalizes a result of Boutet
de
Monvel and
Sjöstrand
for
(0,0)
forms. We introduce a new operator analogous to
the Kohn Laplacian defined on the boundary of a domain and we apply
the heat equation method of Menikoff and
Sjöstrand
to this operator. We
obtain a description of a new
Szegő
projection up to smoothing operators.
Finally, we get our main result by using the
Poisson
operator.
Ce
travail
comporte deux
parties.
Dans la première, nous appliquons
la méthode
de Menikoff-Sjöstrand
au laplacien de Kohn, défini sur
une
varieté CR
compacte orientée connexe et nous obtenons un
développement asymptotique complet du projecteur de
Szegő
pour les
(0,
q) formes quand la forme de
Levi est
non-dégénérée. Cela généralise
un résultat de Boutet de Monvel et
Sjöstrand
pour les
(0,0)
formes. Nous
utilisons des opérateurs intégraux de
Fourier
à phases complexes de
Melin
et
Sjöstrand.
Dans la deuxième partie, nous obtenons un développement asympto¬
tique de la singularité du noyau de Bergman pour les
(0,
q) formes quand
la forme de
Levi est
non-dégénérée. Cela généralise un résultat de Bou¬
tet de Monvel et
Sjöstrand
pour les
(0,0)
formes. Nous introduisons un
nouvel opérateur analogue au laplacien de Kohn défini sur le bord du
domaine, et nous y appliquons la méthode de
Menikoff-Sjöstrand.
Cela
donne une description
modulo
les opérateurs régularisants d'un nouvel
projecteur de
Szegő.
Enfin, nous obtenons notre résultat principal en
utilisant l'opérateur de Poisson. |
| any_adam_object | 1 |
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| id | DE-604.BV037231850 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-16T08:01:21Z |
| institution | BVB |
| isbn | 9782856293041 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021145513 |
| oclc_num | 711826352 |
| open_access_boolean | |
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| owner_facet | DE-703 DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T |
| physical | 8, 131 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Soc. Math. de France |
| record_format | marc |
| series | Mémoires de la SMF |
| series2 | Mémoires de la SMF |
| spelling | Hsiao, Chin-Yu Verfasser (DE-588)143531123 aut Projections in several complex variables Chin-Yu Hsiao Paris Soc. Math. de France 2010 8, 131 S. txt rdacontent n rdamedia nc rdacarrier Mémoires de la SMF 123 Hodge-Theorie (DE-588)4135967-7 gnd rswk-swf Wärmeleitungskern (DE-588)4781182-1 gnd rswk-swf Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd rswk-swf Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 s Wärmeleitungskern (DE-588)4781182-1 s Hodge-Theorie (DE-588)4135967-7 s DE-604 Mémoires de la SMF 123 (DE-604)BV000000921 123 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145513&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145513&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Hsiao, Chin-Yu Projections in several complex variables Mémoires de la SMF Hodge-Theorie (DE-588)4135967-7 gnd Wärmeleitungskern (DE-588)4781182-1 gnd Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd |
| subject_GND | (DE-588)4135967-7 (DE-588)4781182-1 (DE-588)4147400-4 |
| title | Projections in several complex variables |
| title_auth | Projections in several complex variables |
| title_exact_search | Projections in several complex variables |
| title_full | Projections in several complex variables Chin-Yu Hsiao |
| title_fullStr | Projections in several complex variables Chin-Yu Hsiao |
| title_full_unstemmed | Projections in several complex variables Chin-Yu Hsiao |
| title_short | Projections in several complex variables |
| title_sort | projections in several complex variables |
| topic | Hodge-Theorie (DE-588)4135967-7 gnd Wärmeleitungskern (DE-588)4781182-1 gnd Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd |
| topic_facet | Hodge-Theorie Wärmeleitungskern Cauchy-Riemannsche Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145513&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145513&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000921 |
| work_keys_str_mv | AT hsiaochinyu projectionsinseveralcomplexvariables |