Full paper in PDF:
$%S. N. Melikhov, Generalized fourier expansions for distributions and ultradistributions, Rev. Mat. Complut. 12 (1999), no. 2, 349379.%$

Generalized Fourier Expansions for Distributions and Ultradistributions
Sergej N. MELIKHOV
Dept. of Mechanics and Mathematics
Rostov State University
Zerge St. 5
344104 Rostov on Don — Russia

Received: September 23, 1998
Revised: February 24, 1998

ABSTRACT

Let        '
Dw(TTa) be a space of distributions or ultradistributions of Beurling type on the p  -dimensional parallelepiped       prod p            p
TTa :=   j=1[-aj,aj]< R  . We investigate the following problems: 1) When can any element of       '
Dw(TTa) be expanded in absolutely convergent series in a system of generalized exponentials        p
ec(n))n (- N  with special exponents c(n)  ,      p
n  (-  N  . 2) When can a sequence of the coefficients (c )  p
  nn (- N  in an expansion u =  sum    c e
      n (- Np n c(n)  be chosen so that it depends in a continuous and linear way on u (-  Dw(TTa)' , where 0< bj < aj  for all 1 <j < p  .

1991 Mathematics Subject Classification: 46F05,42C15.