Full paper in PDF:
$%S. N. Melikhov, Generalized fourier expansions for distributions and ultradistributions,
Rev. Mat. Complut. 12 (1999), no. 2, 349–379.%$
ABSTRACT
Let be a space of distributions or ultradistributions of Beurling type on the -dimensional parallelepiped . We investigate the following problems: 1) When can any element of be expanded in absolutely convergent series in a system of generalized exponentials with special exponents , . 2) When can a sequence of the coefficients in an expansion be chosen so that it depends in a continuous and linear way on , where for all .
1991 Mathematics Subject Classification: 46F05,42C15.