BOEHMIANS ON THE TORUS

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 $D'({\mathbb{R}}^d)$.

Keywords

• Boehmian;
• Fourier transform;
• distribution

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References

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Cited by

1. An extension of certain integral transform to a space of Boehmians vol.17, 2015, https://doi.org/10.1016/j.jaubas.2014.02.003
2. On the Generalized Krätzel Transform and Its Extension to Bohemian Spaces vol.2013, 2013, https://doi.org/10.1155/2013/841585
3. Stockwell transform for Boehmians vol.24, pp.4, 2013, https://doi.org/10.1080/10652469.2012.686903