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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalization of a theorem of S. N. Bernstein


Author: J. D. Chandler
Journal: Proc. Amer. Math. Soc. 63 (1977), 95-100
MSC: Primary 41A20
MathSciNet review: 0433086
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Abstract: A rational approximation scheme is exhibited for a set $ \Delta $ which consists of a finite union of compact subintervals of the real line. This rational approximation scheme provides a characterization of the analytic functions on $ \Delta $ which generalizes S. N. Bernstein's characterization of the analytic functions on $ [ - 1,1]$.


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

  • [1] S. N. Bernstein, Leçons sur les propriétés extrémales et la meilleure approximation des fonctions analytiques d'une variable réelle, Gauthiers-Villars, Paris, 1926.
  • [2] G. Pólya and G. Szegő, Problems and theorems in analysis. Vol. II, Revised and enlarged translation by C. E. Billigheimer of the fourth German edition, Springer-Verlag, New York-Heidelberg, 1976. Theory of functions, zeros, polynomials, determinants, number theory, geometry; Die Grundlehren der Mathematischen Wissenschaften, Band 216. MR 0396134 (53 #2)
  • [3] Marvin Rosenblum and James Rovnyak, Cayley inner functions and best approximation, J. Approximation Theory 17 (1976), no. 3, 241–253. MR 0613986 (58 #29632)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0433086-6
PII: S 0002-9939(1977)0433086-6
Keywords: Cayley inner function
Article copyright: © Copyright 1977 American Mathematical Society