Boehmians on the torus. (English) Zbl 1132.46029

Nemzer, Dennis

Bull. Korean Math. Soc. 43, No. 4, 831-839 (2006).

Relaxing the conditions on the defining delta sequence, the author constructs and studies a space \(\beta(T^d)\) of Boehmians on the torus that contains the space of distributions as well as the space of hyperfunctions on the torus. He also shows that the Fourier transform is a continuous mapping from \(\beta(T^d)\) onto a subspace of Schwartz distributions, and that a sequence of Boehmians converges if and only if the corresponding sequence of Boehmians converges in \(\mathcal D'(\mathbb R^d)\).

Reviewer: Kim Dohan (Seoul)

MSC:

46F12	Integral transforms in distribution spaces
42B05	Fourier series and coefficients in several variables
44A40	Calculus of Mikusiński and other operational calculi

Keywords:

Boehmian; Fourier transform; distribution