|
Quasianalytic Carleman classes on bounded domains
Author(s):
K.
V.
Trunov;
R.
S.
Yulmukhametov
Translated by:
A. Baranov
Original publication:
Algebra i Analiz,
tom 20
(2008),
nomer 2.
Journal:
St. Petersburg Math. J.
20
(2009),
289-317.
MSC (2000):
Primary 30D60
Posted:
February 4, 2009
MathSciNet review:
2424000
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
Several criteria for the quasianaliticity of Carleman classes at a boundary point of a Jordan domain with rectifiable boundary are found.
References:
-
- 1.
- E. M. Dyn'kin, Pseudoanalytic continuation of smooth functions. Uniform scale, Mathematical Programming and Related Questions (Proc. Seventh Winter School, Drogobych, 1974), Theory of Functions and Functional Analysis, Tsentral. Èkonom.-Mat. Inst. Akad. Nauk SSSR, Moscow, 1976, pp. 40-73. (Russian) MR 0587795 (58:28536)
- 2.
- J. Hadamard, Sur le module maximum d'une fonction et de ses dérivées, C. R. Séances Soc. Math. France 42 (1914).
- 3.
- T. Carleman, Les fonctions quasi analytiques, Paris, 1926.
- 4.
- A. Ostrowski, Über quasianalytische Funktionen und Bestimmtheit asymptotischer Entwickelungen, Acta Math. 53 (1930), 181-266. MR 1555294
- 5.
- S. Mandelbrojt, Séries adhérentes, régularisation des suites, applications, Gauthier-Villars, Paris, 1952. MR 0051893 (14:542f)
- 6.
- Baltasar R.-Salinas, Functions with null moments, Rev. Acad. Ci. Madrid 49 (1955), 331-368. (Spanish) MR 0080174 (18:204e)
- 7.
- B. I. Korenblyum, Quasianalytic classes of functions in a circle, Dokl. Akad. Nauk SSSR 164 (1965), no. 1, 36-39; English transl., Soviet Math. Dokl. 6 (1965), 1155-1158. MR 0212199 (35:3074)
- 8.
- R. S. Yulmukhametov, Quasi-analytical classes of functions in convex domains, Mat. Sb. (N.S.) 130 (172) (1986), no. 4, 500-519; English transl., Math. USSR-Sb. 58 (1987), no. 2, 505-523. MR 0867340 (88a:30076)
- 9.
- -, Approximation of subharmonic functions and applications, Thesis for a Doctor's Degree, Mat. Inst. Akad. Nauk SSSR, Moscow, 1987. (Russian)
- 10.
- J. Sebastião e Silva, Su certe classi di spazi localmente convessi importanti per le applicazioni, Rend. Mat. e Appl. (5) 14 (1955), 388-410. MR 0070046 (16:1122c)
- 11.
- N. Sibony, Approximation polynomiale pondérée dans un domaine d'holomorphie de
 , Ann. Inst. Fourier (Grenoble) 26 (1976), no. 2, 71-99. MR 0430312 (55:3317) - 12.
- M. Brelot, Éléments de la théorie classique du potentiel, Centre Doc. Univ., Paris, 1959. MR 0106366 (21:5099)
- 13.
- A. V. Bitsadze, Foundations of the theory of analytic functions of a complex variable, ``Nauka'', Moscow, 1972. (Russian) MR 0390183 (52:11009)
Similar Articles:
Retrieve articles in St. Petersburg Mathematical Journal
with MSC
(2000):
30D60
Retrieve articles in all Journals with MSC
(2000):
30D60
Additional Information:
K.
V.
Trunov
Affiliation:
Department of Mathematics, Bashkir State University, 450074 Ufa, Russia
Email:
trounovkv@mail.ru
R.
S.
Yulmukhametov
Affiliation:
Department of Mathematics, Bashkir State University, 450074 Ufa, Russia
DOI:
10.1090/S1061-0022-09-01048-6
PII:
S 1061-0022(09)01048-6
Keywords:
Carleman classes,
quasianaliticity
Received by editor(s):
15/AUG/2006
Posted:
February 4, 2009
Additional Notes:
Supported by RFBR (grant no. 06-01-00516-a).
Copyright of article:
Copyright
2009,
American Mathematical Society
|
