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International mathematical journal of analysis and its applications

Editor-in-Chief: Schulz, Friedmar

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Volume 32, Issue 2


Universal interpolation

Andreas Vogt
Published Online: 2013-01-14 | DOI: https://doi.org/10.1524/anly.2012.1126


If Pn is the polynomial of degree at most n-1 which interpolates a function f:[0,1] → ℝat the nodes 0 ≤ xn1 < x2n < ⋯ < xnn ≤ 1 (n ∈ ℕ), it is well-known that, even if f is a continuous function, the sequence (Pn)n ∈ ℕ does not necessarily converge to f. Indeed, for p ∈ [1,∞), there exists an infinitely often differentiable function f and a “nice” system of nodes such that to every measurable function g, there exists a subsequence of (Pn)n ∈ ℕ that converges in Lp to g.

Keywords: universal functions; interpolation

About the article

* Correspondence address: University of Trier, Department of Computer Science and Mathematics, 54286 Trier, Deutschland,

Published Online: 2013-01-14

Published in Print: 2012-06-01

Citation Information: Analysis International mathematical journal of analysis and its applications, Volume 32, Issue 2, Pages 87–96, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1524/anly.2012.1126.

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