Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bernstein approximation problem for differentiable functions and quasi-analytic weights


Author: Guido Zapata
Journal: Trans. Amer. Math. Soc. 182 (1973), 503-509
MSC: Primary 46E10; Secondary 41A65
MathSciNet review: 0343000
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Bernstein problem for differentiable functions is considered. Sufficient conditions in order that a decreasing family of weights be fundamental are given. Some of these conditions are also related to the concept of quasi-analytic weight.


References [Enhancements On Off] (What's this?)

  • [1] J. Horváth, Topological vector spaces and distributions. Vol. 1, Addison-Wesley, Reading, Mass., 1966. MR 34 #4863.
  • [2] S. N. Mergelyan, Weighted approximations by polynomials, Uspehi Mat. Nauk (N.S.) 11 (1956), no. 5(71), 107–152 (Russian). MR 0083614 (18,734c)
  • [3] Leopoldo Nachbin, Elements of approximation theory, Van Nostrand Mathematical Studies, No. 14, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0217483 (36 #572)
  • [4] Leopoldo Nachbin, Silvio Machado, and Jo ao B. Prolla, Weighted approximation, vector fibrations and algebras of operators, J. Math. Pures Appl. (9) 50 (1971), 299–323. MR 0293397 (45 #2474)
  • [5] N. Sibony, Problème de Bernstein pour les fonctions différentiables, Séminaire Choquet, 1969/70, Initiation à l'analyse, fasc. 2, Exposé 12, Secrétariat mathématique, Paris, 1970. MR 43 #6632.
  • [6] G. Zapata, Aproximação ponderada para funções diferenciáveis, Monografias do Centro Brasileiro de Pesquisas Físicas, vol. 30, Rio de Janeiro, 1971.
  • [7] Guido I. Zapata, Sur le problème de Bernstein et les algèbres de fonctions continûment différentiables, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A70–A72 (French). MR 0291707 (45 #798)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E10, 41A65

Retrieve articles in all journals with MSC: 46E10, 41A65


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0343000-0
PII: S 0002-9947(1973)0343000-0
Keywords: Bernstein problem for differentiable functions, fundamental family of weights, decreasing family, quasi-analytic
Article copyright: © Copyright 1973 American Mathematical Society