Boehmians on the torus
Bull. Korean Math. Soc. 2006 Vol. 43, No. 4, 831-839
Published online December 1, 2006
Dennis Nemzer
California State University
Abstract : 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
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