Approximation by polynomials in a weighted space of infinitely differentiable functions

Details Approximation by polynomials in a weighted space of infinitely differentiable functions Approximation by polynomials in a weighted space of infinitely differentiable functions

2005-08-26

arxiv.org/abs/math/0508524v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result for description of strong dual for weighted spaces of infinitely differentiable functions on real line and weighted spaces of sequences of infinitely differentiable functions on real line in terms of the Fourier-Laplace transform of functionals.

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