Quasianalytic Carleman classes on bounded domains
HTML articles powered by AMS MathViewer
- by
K. V. Trunov and R. S. Yulmukhametov
Translated by: A. Baranov - St. Petersburg Math. J. 20 (2009), 289-317
- DOI: https://doi.org/10.1090/S1061-0022-09-01048-6
- Published electronically: February 4, 2009
- PDF | Request permission
Abstract:
Several criteria for the quasianaliticity of Carleman classes at a boundary point of a Jordan domain with rectifiable boundary are found.References
- E. M. Dyn′kin, Pseudoanalytic continuation of smooth functions. Uniform scale, Mathematical programming and related questions (Proc. Seventh Winter School, Drogobych, 1974) Central. Èkonom.-Mat. Inst. Akad. Nauk SSSR, Moscow, 1976, pp. 40–73 (Russian). MR 0587795
- J. Hadamard, Sur le module maximum d’une fonction et de ses dérivées, C. R. Séances Soc. Math. France 42 (1914).
- T. Carleman, Les fonctions quasi analytiques, Paris, 1926.
- Alexander Ostrowski, Über quasianlytische Funktionen und Bestimmtheit asymptotischer Entwickleungen, Acta Math. 53 (1929), no. 1, 181–266 (German). MR 1555294, DOI 10.1007/BF02547570
- S. Mandelbrojt, Séries adhérentes, régularisation des suites, applications, Gauthier-Villars, Paris, 1952 (French). MR 0051893
- Baltasar R.-Salinas, Functions with null moments, Rev. Acad. Ci. Madrid 49 (1955), 331–368 (Spanish). MR 80174
- B. I. Korenbljum, Quasianalytic classes of functions in a circle, Dokl. Akad. Nauk SSSR 164 (1965), 36–39 (Russian). MR 0212199
- R. S. Yulmukhametov, Quasi-analytical classes of functions in convex domains, Mat. Sb. (N.S.) 130(172) (1986), no. 4, 500–519, 575–576 (Russian); English transl., Math. USSR-Sb. 58 (1987), no. 2, 505–523. MR 867340, DOI 10.1070/SM1987v058n02ABEH003117
- —, Approximation of subharmonic functions and applications, Thesis for a Doctor’s Degree, Mat. Inst. Akad. Nauk SSSR, Moscow, 1987. (Russian)
- José Sebastião e Silva, Su certe classi di spazi localmente convessi importanti per le applicazioni, Rend. Mat. e Appl. (5) 14 (1955), 388–410 (Italian). MR 70046
- Nessim Sibony, Approximation polynomiale pondérée dans un domaine d’holomorphie de $\textbf {C}^{n}$, Ann. Inst. Fourier (Grenoble) 26 (1976), no. 2, x, 71–99. MR 430312
- M. Brelot, Éléments de la théorie classique du potentiel, “Les Cours de Sorbonne”, vol. 3, Centre de Documentation Universitaire, Paris, 1959 (French). MR 0106366
- A. V. Bitsadze, Osnovy teorii analiticheskikh funktsiĭ kompleksnogo peremennogo, Izdat. “Nauka”, Moscow, 1972 (Russian). Second edition, augmented. MR 0390183
Bibliographic 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
- Received by editor(s): August 15, 2006
- Published electronically: February 4, 2009
- Additional Notes: Supported by RFBR (grant no. 06-01-00516-a).
- © Copyright 2009 American Mathematical Society
- Journal: St. Petersburg Math. J. 20 (2009), 289-317
- MSC (2000): Primary 30D60
- DOI: https://doi.org/10.1090/S1061-0022-09-01048-6
- MathSciNet review: 2424000