Boehmians of type S and their Fourier transforms

R. Bhuvaneswari; V. Karunakaran

Annales UMCS, Mathematica (2010)

  • Volume: 64, Issue: 1, page 27-43
  • ISSN: 2083-7402

Abstract

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Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.

How to cite

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R. Bhuvaneswari, and V. Karunakaran. " Boehmians of type S and their Fourier transforms ." Annales UMCS, Mathematica 64.1 (2010): 27-43. <http://eudml.org/doc/267973>.

@article{R2010,
abstract = {Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.},
author = {R. Bhuvaneswari, V. Karunakaran},
journal = {Annales UMCS, Mathematica},
keywords = {Boehmians; spaces of type S; Fourier transform; spaces of type },
language = {eng},
number = {1},
pages = {27-43},
title = { Boehmians of type S and their Fourier transforms },
url = {http://eudml.org/doc/267973},
volume = {64},
year = {2010},
}

TY - JOUR
AU - R. Bhuvaneswari
AU - V. Karunakaran
TI - Boehmians of type S and their Fourier transforms
JO - Annales UMCS, Mathematica
PY - 2010
VL - 64
IS - 1
SP - 27
EP - 43
AB - Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
LA - eng
KW - Boehmians; spaces of type S; Fourier transform; spaces of type
UR - http://eudml.org/doc/267973
ER -

References

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  1. Chung, J., Chung, S. Y. and Kim, D., A characterization of the Gelfand-Shilov spaces via Fourier transform, Prod. Amer. Math. Soc. 124 (1996), 2101-2108.[Crossref] Zbl0871.46018
  2. Chung, S. Y., Kim, D. and Lee, S., Characterization for Beurling-Bjorck space and Schwartz space, Prod. Amer. Math. Soc. 125 (11) (1997), 3229-3234.[Crossref] Zbl0887.46013
  3. Gelfand, I. M., Shilov, G. E., Generalized Functions, Vol. I and II, Academic Press, New York, 1967. 
  4. Ishihara, T., On the structure of S space, Osaka Math. J. 13 (1961), 251-264. Zbl0109.08201
  5. Kashpirovskii, A. I., Equality of the spaces Sβα and Sα ∩ Sβ, (English. Russian original) Funct. Anal. Appl. 14, 129 (1980); translation from Funkts. Anal. Prilozh. 14, No.2, 60 (1980).[Crossref] 
  6. Karunakaran, V., Kalpakam, N. V., Boehmians and Fourier transform, Integral Transform. Spec. Funct. 9 (3) (2000), 197-216.[Crossref] Zbl0980.46027
  7. Mikusinski, P., Convergence of Boehmians, Japan J. Math. 9 (1983), 159-179. Zbl0524.44005
  8. Mikusinski, P., Boehmians and generalized functions, Acta. Math. Hung. 51 (1988), 271-281.[Crossref] Zbl0652.44005
  9. Zemanian, A. H., Distribution Theory and Transform Analysis, McGraw-Hill Book Co., New York, 1965. Zbl0127.07201

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