RMC - Vol. 12, Num. 2 - Sergej N. Melikhov

Full paper in PDF:
$%S. N. Melikhov, Generalized fourier expansions for distributions and ultradistributions, Rev. Mat. Complut. 12 (1999), no. 2, 349–379.%$

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

melih@ms.math.rsu.ru

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.