A generalization of a theorem of S. N. Bernstein
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- by J. D. Chandler PDF
- Proc. Amer. Math. Soc. 63 (1977), 95-100 Request permission
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
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S. N. Bernstein, Leçons sur les propriétés extrémales et la meilleure approximation des fonctions analytiques d’une variable réelle, Gauthiers-Villars, Paris, 1926.
- 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, Die Grundlehren der mathematischen Wissenschaften, Band 216, Springer-Verlag, New York-Heidelberg, 1976. Theory of functions, zeros, polynomials, determinants, number theory, geometry. MR 0396134
- Marvin Rosenblum and James Rovnyak, Cayley inner functions and best approximation, J. Approximation Theory 17 (1976), no. 3, 241–253. MR 613986, DOI 10.1016/0021-9045(76)90087-3
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 95-100
- MSC: Primary 41A20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0433086-6
- MathSciNet review: 0433086