## Boehmians on the torus.(English)Zbl 1132.46029

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
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