Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On $(0,1,2)$ interpolation in uniform metric
HTML articles powered by AMS MathViewer

by J. Szabados and A. K. Varma PDF
Proc. Amer. Math. Soc. 109 (1990), 975-979 Request permission

Abstract:

From the well known theorem of G. Faber it follows that for any given matrix of nodes there exists a continuous function for which the Lagrange interpolation polynomial ${L_n}[f,x]$, generated by the $n$ th row of the matrix, does not tend uniformly to $f(x)$. In this paper we shall provide analogous results for the related operator ${H_{n,3}}[f,x]$ as defined below.
References
  • P. Erdös, On the uniform distribution of the roots of certain polynomials, Ann. of Math. (2) 43 (1942), 59–64. MR 5947, DOI 10.2307/1968879
  • P. Erdös and P. Turán, On interpolation. I, Ann. of Math. 38 (1937), 142-155.
  • P. Erdős and P. Turán, An extremal problem in the theory of interpolation, Acta Math. Acad. Sci. Hungar. 12 (1961), 221–234 (English, with Russian summary). MR 146571, DOI 10.1007/BF02066685
  • G. Faber, Über die interpolatorische Darstellung stetiger Funktionen, Jahresber. der Deutschen Math. Ver. 23 (1914), 190-210.
  • Ryozi Sakai, Hermite-Fejér interpolation prescribing higher order derivatives, Progress in approximation theory, Academic Press, Boston, MA, 1991, pp. 731–759. MR 1114810
  • Gábor Szegő, Orthogonal polynomials, 3rd ed., American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1967. MR 0310533
  • P. Vértesi, Hermite-Fejér interpolations of higher order. I, Acta Math. Hungar. 54 (1989), no. 1-2, 135–152. MR 1015784, DOI 10.1007/BF01950715
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A05, 41A10
  • Retrieve articles in all journals with MSC: 41A05, 41A10
Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 109 (1990), 975-979
  • MSC: Primary 41A05; Secondary 41A10
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1013983-X
  • MathSciNet review: 1013983