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Universal interpolation
Published/Copyright:
January 14, 2013
Abstract
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
Published Online: 2013-01-14
Published in Print: 2012-06
© by Oldenbourg Wissenschaftsverlag, Trier, Germany
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Articles in the same Issue
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- Generalized Boyd´s indices and applications
- A problem in analysis
- New sequences that converge to a generalized Euler constant
- A uniform version of Laplace´s method for contour integrals
- Representation of multipliers on spaces of real analytic functions
- Infinite pseudo-differential operators on WM(Rn) space
- Erratum to: Approximation schemes for solving disturbed control problems with non-terminal time and state constraints
