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Paper's Title:

On Interpolation of L2 functions


Anis Rezgui

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

Mathematics Department,
University of Carthage, Tunis,


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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