Bulletin of the Korean Mathematical Society ( Vol.43 NO.4 / 2006 ) Title Boehmians on the torus(ENG) Author Dennis Nemzer MSC 44A40, 46F12, 42B05 Publication Page 831-839 Page Abstract 1. Introduction 2. Notation and the space $eta_TT$ 3. The space $eta(T^d)$ 4. Convergence Own Status Keyword Boehmian, Fourier transform, distribution Note Summary By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus $eta(T^d)$ is constructed and studied. The space $eta(T^d)$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from $eta(T^d)$ onto a subspace of Schwartz distributions. The range of the Fourier transform is characterized. A necessary and sufficient condition for a sequence of Boehmians to converge is that the corresponding sequence of Fourier transforms converges in $mathcal{D}'(RR^d)$. Attach [DVI]  [PDF]