Resumen de Generalized Fourier expansions for distributions and ultradistributions

S.N. Melikhov

• Let Dw(Pa)' be a space of distributions or ultradistributions of Beurling type on the p-dimensional parallelepiped Pa:=Ppj=1[-aj,aj]ÌRp. We investigate the following problems:

  1) When can any element of Dw(Pa)' be expanded in absolutely convergent series in a system of generalized exponentials (el(n))nÎNp with special exponents l(n), nÎNp.

  2) When can a sequence of the coefficients (cn)nÎNp in an expansionu=SnÎNp cnel(n) be chosen so that it depends in a continuous and linear way on uÎDw(Pa)', where 0