Local analytic classification of q-difference equations:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Soc. Math. de France
2013
|
| Series: | Astérisque
355 |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | VI, 151 S. |
| ISBN: | 9782856297759 |
Staff View
MARC
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| 245 | 1 | 0 | |a Local analytic classification of q-difference equations |c Jean-Pierre Ramis ; Jacques Sauloy ; Changgui Zhang |
| 264 | 1 | |a Paris |b Soc. Math. de France |c 2013 | |
| 300 | |a VI, 151 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Sauloy, Jacques |d 1953- |e Verfasser |0 (DE-588)1048245764 |4 aut | |
| 700 | 1 | |a Zhang, Changgui |e Verfasser |0 (DE-588)1050054652 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027171234 | ||
Record in the Search Index
| _version_ | 1804152004105207808 |
|---|---|
| adam_text | CONTENTS
1.
Introduction
............................................................... 1
1.1.
The problem
............................................................ 1
1.2.
Contents of the paper
................................................... 3
1.3.
General notations
.......................................................
(j
Acknowledgements
........................................................... 8
2.
Some general nonsense
................................................... 9
2.1.
The category of g-difference modules
.................................... 9
2.2.
The Newton polygon and the slope nitration
............................ 13
2.3.
Application to the analytic
isoformal
classification ......................
18
3.
The
affine
space of
isoforma]
analytic classes
.......................... 25
3.1. Isoformal
analytic classes of analytic (/-difference modules
............... 25
3.2.
Index theorems and irregularity
......................................... 28
3.3.
Explicit description of
Т(Р
.....
Pk)
in the case of integral slopes
....... 31
3.4.
Interpolation by g-Gevrey classes
........................................ 36
4.
The (/-analogs of Birkhoff-Malgrange-Sibuya theorems
............... 39
4.1.
Asymptotics
............................................................. 39
4.2.
Existence of asymptotic solutions
....................................... 45
4.3.
The fundamental isomorphism
.......................................... 48
4.4.
The
isoformal
classification by the cohomology of the Stokes sheaf
...... 55
5.
Summation and asymptotic theory
..................................... 59
5.1.
Some preparatory notations and results
................................. 59
5.2.
Asymptotics relative to a divisor
........................................ 64
5.3.
(/-Gevrey theorem of Borel-Ritt and flat functions
....................... 73
5.4.
Relative divisors and multisuinmable functions
.......................... 78
5.5.
Analytic classification of linear (/-difference equations
................... 81
vi
CONTENTS
6.
Geometry of the space of classes
........................................ 87
6.1.
Privileged cocycles
...................................................... 87
6.2.
Dévissage q-Gevrey
...................................................... 91
6.3.
Vector bundles associated to
ç-difference modules
....................... 95
7.
Examples of the Stokes phenomenon
................................... 97
7.1.
The q-Euler equation and confluent basic hypergeometric series
......... 98
7.2.
Ttie symmetric square of the q-Euler equation
...........................103
7.3.
From the Mock
T het
a functions to the
q-Euler
equation
................107
7.4.
From class numbers of quadratic forms to the g-Euler equation
.........
Ill
A. Classification of isograded filtered difference modules
...............113
A.I. General sett ing of the problem
..........................................113
Л.2.
Difference modules over difference rings
.................................116
Л.З.
Finitely filtered difference modules
......................................122
A.I. Extensions of difference modules
........................................125
Л.5.
Extension of sealers
.....................................................129
A.(t. Our moduli space
.......................................................131
A.
7.
Extension classes of difference modules
.................................133
A.S. The cohomological equation
............................................135
Bibliography
..................................................................139
Index of notations
...........................................................145
Index
..........................................................................149
ASTÉRISQIE
»55
We essentially achieve Birkhoff s program for (/-difference equa¬
tions by giving three different descriptions of the moduli space of
isoformal
analytic classes. This involves an extension of Birkhoff-
Guenther normal forms, (/-analogues of the so-called Birkhoff-
Malgrange-Sibuya theorems and a new theory of summation.
The results were announced in
La variété des
classes
analy¬
tiques d équations aux (/-différences dans une classe formelle and
Développement asymptotique et sommabilité des solutions des
équations linéaires aux (/-différences
and in various seminars and
.
conferences between
2004
and
2006.
|
| any_adam_object | 1 |
| author | Ramis, Jean-Pierre 1943- Sauloy, Jacques 1953- Zhang, Changgui |
| author_GND | (DE-588)1048629414 (DE-588)1048245764 (DE-588)1050054652 |
| author_facet | Ramis, Jean-Pierre 1943- Sauloy, Jacques 1953- Zhang, Changgui |
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| author_sort | Ramis, Jean-Pierre 1943- |
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| bvnumber | BV041724339 |
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| ctrlnum | (OCoLC)872347025 (DE-599)HBZHT018191157 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041724339 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:03:49Z |
| institution | BVB |
| isbn | 9782856297759 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027171234 |
| oclc_num | 872347025 |
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| owner_facet | DE-83 DE-19 DE-BY-UBM DE-824 DE-384 DE-355 DE-BY-UBR DE-29T |
| physical | VI, 151 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Soc. Math. de France |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spelling | Ramis, Jean-Pierre 1943- Verfasser (DE-588)1048629414 aut Local analytic classification of q-difference equations Jean-Pierre Ramis ; Jacques Sauloy ; Changgui Zhang Paris Soc. Math. de France 2013 VI, 151 S. txt rdacontent n rdamedia nc rdacarrier Astérisque 355 Sauloy, Jacques 1953- Verfasser (DE-588)1048245764 aut Zhang, Changgui Verfasser (DE-588)1050054652 aut Astérisque 355 (DE-604)BV002579439 355 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027171234&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027171234&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Ramis, Jean-Pierre 1943- Sauloy, Jacques 1953- Zhang, Changgui Local analytic classification of q-difference equations Astérisque |
| title | Local analytic classification of q-difference equations |
| title_auth | Local analytic classification of q-difference equations |
| title_exact_search | Local analytic classification of q-difference equations |
| title_full | Local analytic classification of q-difference equations Jean-Pierre Ramis ; Jacques Sauloy ; Changgui Zhang |
| title_fullStr | Local analytic classification of q-difference equations Jean-Pierre Ramis ; Jacques Sauloy ; Changgui Zhang |
| title_full_unstemmed | Local analytic classification of q-difference equations Jean-Pierre Ramis ; Jacques Sauloy ; Changgui Zhang |
| title_short | Local analytic classification of q-difference equations |
| title_sort | local analytic classification of q difference equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027171234&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=027171234&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
| work_keys_str_mv | AT ramisjeanpierre localanalyticclassificationofqdifferenceequations AT sauloyjacques localanalyticclassificationofqdifferenceequations AT zhangchanggui localanalyticclassificationofqdifferenceequations |