Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Quasianalytic Carleman classes on bounded domains

Authors: K. V. Trunov and 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
Published electronically: February 4, 2009
MathSciNet review: 2424000
Full-text 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 [Enhancements On Off] (What's this?)

  • 1. 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
  • 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. Alexander Ostrowski, Über quasianlytische Funktionen und Bestimmtheit asymptotischer Entwickleungen, Acta Math. 53 (1929), no. 1, 181–266 (German). MR 1555294,
  • 5. S. Mandelbrojt, Séries adhérentes, régularisation des suites, applications, Gauthier-Villars, Paris, 1952 (French). MR 0051893
  • 6. Baltasar R.-Salinas, Functions with null moments, Rev. Acad. Ci. Madrid 49 (1955), 331–368 (Spanish). MR 0080174
  • 7. B. I. Korenbljum, Quasianalytic classes of functions in a circle, Dokl. Akad. Nauk SSSR 164 (1965), 36–39 (Russian). MR 0212199
  • 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. 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 0070046
  • 11. Nessim Sibony, Approximation polynomiale pondérée dans un domaine d’holomorphie de 𝐶ⁿ, Ann. Inst. Fourier (Grenoble) 26 (1976), no. 2, x, 71–99. MR 0430312
  • 12. M. Brelot, Éléments de la théorie classique du potentiel, Les Cours de Sorbonne. 3e cycle, Centre de Documentation Universitaire, Paris, 1959 (French). MR 0106366
  • 13. A. V. Bitsadze, \cyr Osnovy teorii analiticheskikh funktsiĭ kompleksnogo peremennogo., Izdat. “Nauka”, Moscow, 1972 (Russian). Second edition, augmented. MR 0390183

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

R. S. Yulmukhametov
Affiliation: Department of Mathematics, Bashkir State University, 450074 Ufa, Russia

Keywords: Carleman classes, quasianaliticity
Received by editor(s): August 15, 2006
Published electronically: February 4, 2009
Additional Notes: Supported by RFBR (grant no. 06-01-00516-a).
Article copyright: © Copyright 2009 American Mathematical Society

American Mathematical Society