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http://dx.doi.org/10.4134/BKMS.2006.43.4.831

BOEHMIANS ON THE TORUS  

Nemzer, Dennis (DEPARTMENT OF MATHEMATICS, CALIFORNIA STATE UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.4, 2006 , pp. 831-839 More about this Journal
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.
Keywords
Boehmian; Fourier transform; distribution;
Citations & Related Records

Times Cited By SCOPUS : 1
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1 J. Burzyk, P. Mikusinski, and D. Nemzer, Remarks on topological properties of Boehmians, Rocky Mountain J. Math. 35 (2005), no. 3, 727-740   DOI   ScienceOn
2 P. Mikusinski, Tempered Boehmians and ultradistributions. Proc. Amer. Math. Soc. 123 (1995), 813-817
3 P. Mikusinski, Boehmians on manifolds, Internat. J. Math. Math. Sci. 24 (2000), no. 9, 583-588   DOI
4 D. Nemzer, Periodic Boehmians, Internat. J. Math. Math. Sci. 12 (1989), 685-692   DOI   ScienceOn
5 D. Nemzer, Periodic Boehmians II, Bull. Austral. Math. Soc. 44 (1991), 271-278   DOI
6 A. Zygmund, Trigonometric Series (2nd Edition), Vol. I, II, Cambridge University Press, New York, 1959
7 I. M. Gelfand and G. E. Shilov, Generalized Functions, Vol. 1,2, Academic Press, New York, 1964/1968