Quasipower series and quasianalytic classes of functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
2002
|
| Series: | Translations of mathematical monographs
216 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 183 S. graph. Darst. |
| ISBN: | 0821829432 |
Staff View
MARC
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| 240 | 1 | 0 | |a Kvazistepennye rjady i kvazianaliticeskie klassy funkcij |
| 245 | 1 | 0 | |a Quasipower series and quasianalytic classes of functions |c G. V. Badalyan |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2002 | |
| 300 | |a XIII, 183 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 7 | |a FUNÇÕES DE UMA VARIÁVEL COMPLEXA |2 larpcal | |
| 650 | 4 | |a Fonctions quasi analytiques | |
| 650 | 7 | |a SÉRIES INFINITAS |2 larpcal | |
| 650 | 4 | |a Séries infinies | |
| 650 | 4 | |a Quasianalytic functions | |
| 650 | 4 | |a Series, Infinite | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vii
Introduction
ix
Chapter
1.
Quasianalytic classes of functions
1
§1.
Watson s problem
1
§2.
A version of the criterion for uniqueness of the solution to Watson s
problem
6
§3.
Carleman s theorem on quasianalyticity of a class of functions
9
§4.
Carleman s theorem on representation of functions of a quasiana¬
lytic class. Bang s formula
11
§5.
Factorial series
16
§6.
The
Lagrange
identities
24
Chapter
2.
Generalizations of the Taylor formula.
Quasipower
series
27
§1.
A generalization of the Taylor formula
27
§2.
Properties of the quasipower series in the basic interval
37
§3.
On the term-by-term differentiation of a quasipower series in the
basic interval
58
Chapter
3.
Functions of Carleman s classes: Expansion in quasipower series
63
§1.
The order of uniform convergence of a quasipower series; relation
to factorial series
63
§2.
On a transformation of the quasipower series
69
§3.
Legendre polynomials and quasipolynomials. Estimation of their
successive generalized derivatives
75
§4.
Sufficient condition for functions of Carleman s classes to admit an
expansion in the corresponding quasipower series
81
Chapter
4.
Criteria for the possibility of expanding functions in quasipower
and factorial series
89
§1.
Classes T7)J<(0,ii] and C7jJ<(0, u] and the criterion for expanding
functions in quasipower series
89
§2.
Quasianalytic characterization of the class C7j>t(0,u] and a crite¬
rion for the possibility of expanding functions in quasipower series.
Application to factorial series
102
§3.
Non-quasianalytic classes C7jX(0,it] and
AC7¡>c(0,u]
107
§4.
On the comparison between classes C7)>c(0,
1]
and
C7/)Jť(0,
1] 114
Chapter
5.
Generalized completely monotone functions and the condition
for absolute convergence of a quasipower series (in the basic in¬
terval)
119
§1.
Quasianalytic characteristic of the class
i?7(0,u)
and the condition
for absolute convergence of a quasipower series
120
§2.
Functions of class
Д7(0, оо)
129
Chapter
6.
On the use of quasipower series for representation of analytic
functions in non-circular domains
139
§1.
Introduction
139
§2.
Representation of a function by a quasipower series with respect
to the system {{za
-
l)k} in za
-
1|
< 1,
a
> 1 141
§3.
Representation of a function by a quasipower series with respect
to the system
{{ζδ
-
l)fc} in zs
-
1|
< 1,
б Є
[§, 1] 145
§4.
Conditions for analyticity of function
φ(ζ)
in ]zs
—
1|
< 1,
<
б
<
1,
in terms of its ordinary derivatives at zq
= 1 150
Chapter
7.
Some applications of quasipower series to the theory of functions
of quasianalytic classes
153
§1.
Factorial series as a tool for summation of asymptotic series
155
§2.
Quasianalytic continuation of a function. Relation to
de la Vallée-
Poussin s problem
163
§3.
Solution to Borel s problem in the classes
C7)Jť(0, v]
165
Bibliography
181
|
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.243 |
| dewey-search | 515/.243 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023836664 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:43Z |
| institution | BVB |
| isbn | 0821829432 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017478784 |
| oclc_num | 50598256 |
| open_access_boolean | |
| owner | DE-634 DE-739 |
| owner_facet | DE-634 DE-739 |
| physical | XIII, 183 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Badalian, Gajk V. Verfasser aut Kvazistepennye rjady i kvazianaliticeskie klassy funkcij Quasipower series and quasianalytic classes of functions G. V. Badalyan Providence, RI American Math. Soc. 2002 XIII, 183 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 216 FUNÇÕES DE UMA VARIÁVEL COMPLEXA larpcal Fonctions quasi analytiques SÉRIES INFINITAS larpcal Séries infinies Quasianalytic functions Series, Infinite Quasianalytische Funktion (DE-588)4294372-3 gnd rswk-swf Reihe (DE-588)4049197-3 gnd rswk-swf Reihe (DE-588)4049197-3 s Quasianalytische Funktion (DE-588)4294372-3 s DE-604 Translations of mathematical monographs 216 (DE-604)BV000002394 216 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478784&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Badalian, Gajk V. Quasipower series and quasianalytic classes of functions Translations of mathematical monographs FUNÇÕES DE UMA VARIÁVEL COMPLEXA larpcal Fonctions quasi analytiques SÉRIES INFINITAS larpcal Séries infinies Quasianalytic functions Series, Infinite Quasianalytische Funktion (DE-588)4294372-3 gnd Reihe (DE-588)4049197-3 gnd |
| subject_GND | (DE-588)4294372-3 (DE-588)4049197-3 |
| title | Quasipower series and quasianalytic classes of functions |
| title_alt | Kvazistepennye rjady i kvazianaliticeskie klassy funkcij |
| title_auth | Quasipower series and quasianalytic classes of functions |
| title_exact_search | Quasipower series and quasianalytic classes of functions |
| title_full | Quasipower series and quasianalytic classes of functions G. V. Badalyan |
| title_fullStr | Quasipower series and quasianalytic classes of functions G. V. Badalyan |
| title_full_unstemmed | Quasipower series and quasianalytic classes of functions G. V. Badalyan |
| title_short | Quasipower series and quasianalytic classes of functions |
| title_sort | quasipower series and quasianalytic classes of functions |
| topic | FUNÇÕES DE UMA VARIÁVEL COMPLEXA larpcal Fonctions quasi analytiques SÉRIES INFINITAS larpcal Séries infinies Quasianalytic functions Series, Infinite Quasianalytische Funktion (DE-588)4294372-3 gnd Reihe (DE-588)4049197-3 gnd |
| topic_facet | FUNÇÕES DE UMA VARIÁVEL COMPLEXA Fonctions quasi analytiques SÉRIES INFINITAS Séries infinies Quasianalytic functions Series, Infinite Quasianalytische Funktion Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478784&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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