  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.
