Boehmians of type S and their Fourier transforms

R. Bhuvaneswari; V. Karunakaran

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2010)

  • Volume: 54, Issue: 1
  • ISSN: 0365-1029

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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 54.1 (2010): null. <http://eudml.org/doc/289830>.

@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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Boehmians; spaces of type S; Fourier transform},
language = {eng},
number = {1},
pages = {null},
title = {Boehmians of type S and their Fourier transforms},
url = {http://eudml.org/doc/289830},
volume = {54},
year = {2010},
}

TY - JOUR
AU - R. Bhuvaneswari
AU - V. Karunakaran
TI - Boehmians of type S and their Fourier transforms
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2010
VL - 54
IS - 1
SP - null
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
UR - http://eudml.org/doc/289830
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. 
  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. 
  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. 
  5. Kashpirovskii, A. I., Equality of the spaces S α β and S α ∩ S β , (English. Russian original) Funct. Anal. Appl. 14, 129 (1980); translation from Funkts. Anal. Prilozh. 14, No.2, 
  6. 60 (1980). 
  7. Karunakaran, V., Kalpakam, N. V., Boehmians and Fourier transform, Integral Transform. Spec. Funct. 9 (3) (2000), 197-216. 
  8. Mikusiński, P., Convergence of Boehmians, Japan J. Math. 9 (1983), 159-179. 
  9. Mikusiński, P., Boehmians and generalized functions, Acta. Math. Hung. 51 (1988), 271-281. 
  10. Zemanian, A. H., Distribution Theory and Transform Analysis, McGraw-Hill Book Co., New York, 1965. 

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