Paper Title:

On Interpolation of L² functions

Author(s):

Anis Rezgui

Department of Mathematics,
Faculty of Sciences,
Taibah University, Al Madina Al Munawara,
KSA.

Mathematics Department,
INSAT,
University of Carthage, Tunis,
Tunisia
E-mail: anis.rezguii@gmail.com

Abstract:

In this paper we are interested in polynomial interpolation of irregular functions namely those elements of L²(R,μ) for μ a given probability measure. This is of course doesn't make any sense unless for L² functions that, at least, admit a continuous version. To characterize those functions we have, first, constructed, in an abstract fashion, a chain of Sobolev like subspaces of a given Hilbert space H₀. Then we have proved that the chain of Sobolev like subspaces controls the existence of a continuous version for L² functions and gives a pointwise polynomial approximation with a quite accurate error estimation.

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