×

Converse results in the Walsh theory of overconvergence. (English) Zbl 0578.41003

Summary: Recently, J. Szabados has obtained a new converse theorem in the Walsh overconvergence theory, based on Lagrange interpolation. Here, we similarly develop a related converse theorem, based on Hermite interpolation, which generalizes Szabados’ result.

MSC:

41A05 Interpolation in approximation theory
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] A. S. CAVARETTA, Jr., A. SHARMA and R. S. Varga, An extension of a theorem of J. L. Walsh, Resultate der Mathematik 3 (1980), 155-191. Zbl0447.30020 MR600999 · Zbl 0447.30020 · doi:10.1007/BF03323355
[2] T. J. RIVLIN, On Walsh equiconvergence, J. Approximation Theory 36 (1982), 334-345. Zbl0504.42016 MR682176 · Zbl 0504.42016 · doi:10.1016/0021-9045(82)90053-3
[3] E. B. SAFF and R. S. VARGA, A note on the sharpness of J. L. Walsh’s Theorem and its extensions for interpolation in the roots of unity, Acta Math. Hung. 43 (1983), 371-377. Zbl0524.30026 MR703748 · Zbl 0524.30026 · doi:10.1007/BF01961323
[4] J. SZABADOS, Converse results in the theory of overconvergence of complex inter-polating polynomials, Analysis 2 (1982), 267-280. Zbl0532.30002 MR732335 · Zbl 0532.30002
[5] R. S. VARGA, Topics in Polynomial and Rational Interpolation and Approximation, University of Montreal Press, 1982. Zbl0484.30023 MR654329 · Zbl 0484.30023
[6] J. L. WALSH, Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc. Colloquium Publications Volume XX, Providence, RI, fifth edition, 1969. Zbl0146.29902 MR218588 JFM61.0315.01 · Zbl 0146.29902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.