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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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
  • [3] Marvin Rosenblum and James Rovnyak, Cayley inner functions and best approximation, J. Approximation Theory 17 (1976), no. 3, 241–253. MR 0613986

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A20

Retrieve articles in all journals with MSC: 41A20


Additional Information

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