Bulletin of the
Korean Mathematical Society BKMS

By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus $\beta(T^d)$ is constructed and studied. The space $\beta(T^d)$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from $\beta(T^d)$ 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 $\mathcal{D}'(\RR^d)$.

Keywords: Boehmian, Fourier transform, distribution

MSC numbers: 44A40, 46F12, 42B05