BOEHMIANS ON THE TORUS

Title & Authors
BOEHMIANS ON THE TORUS
Nemzer, Dennis;

Abstract
By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus $\small{{\beta}(T^d)}$ is constructed and studied. The space $\small{{\beta}(T^d)}$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from $\small{{\beta}(T^d)}$ 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 $\small{D$.
Keywords
Boehmian;Fourier transform;distribution;
Language
English
Cited by
1.
An extension of certain integral transform to a space of Boehmians, Journal of the Association of Arab Universities for Basic and Applied Sciences, 2015, 17, 36
2.
On the Generalized Krätzel Transform and Its Extension to Bohemian Spaces, Abstract and Applied Analysis, 2013, 2013, 1
3.
Stockwell transform for Boehmians, Integral Transforms and Special Functions, 2013, 24, 4, 251
References
1.
J. Burzyk, P. Mikusinski, and D. Nemzer, Remarks on topological properties of Boehmians, Rocky Mountain J. Math. 35 (2005), no. 3, 727-740

2.
I. M. Gelfand and G. E. Shilov, Generalized Functions, Vol. 1,2, Academic Press, New York, 1964/1968

3.
P. Mikusinski, Tempered Boehmians and ultradistributions. Proc. Amer. Math. Soc. 123 (1995), 813-817

4.
P. Mikusinski, Boehmians on manifolds, Internat. J. Math. Math. Sci. 24 (2000), no. 9, 583-588

5.
D. Nemzer, Periodic Boehmians, Internat. J. Math. Math. Sci. 12 (1989), 685-692

6.
D. Nemzer, Periodic Boehmians II, Bull. Austral. Math. Soc. 44 (1991), 271-278

7.
A. Zygmund, Trigonometric Series (2nd Edition), Vol. I, II, Cambridge University Press, New York, 1959