Spaces of Distributions and Interpolation by Translates of a Basis Function
نویسندگان
چکیده
Interpolation with translates of a basis function is a common process in approximation theory. One starts with a single function (the basis function) and a set of interpolation points. The most elementary form of the interpolant then consists of a linear combination of all translates by interpolation points of the basis function. Frequently , low degree polynomials are added to the interpolant. One of the signiicant features of this type of interpolant is that it is often the solution of a variational problem. To make this work, one needs an appropriate space in which to carry out the variational arguments. In this paper we concentrate on developing such spaces for a wide class of basis functions. We also show how the theory leads to eecient ways of calculating the interpolant and to error estimates.
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