Boehmians of type S and their Fourier transforms

• Autorzy: R. Bhuvaneswari , V. Karunakaran
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Boehmians; spaces of type S; Fourier transform

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2010
• Tom: 54
• Numer: 1

Daty

wydano

2010

online

2016-07-29

Twórcy

autor

R. Bhuvaneswari

autor

V. Karunakaran

Bibliografia

• 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.
• 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.
• Gelfand, I. M., Shilov, G. E., Generalized Functions, Vol. I and II, Academic Press, New York, 1967.
• Ishihara, T., On the structure of S space, Osaka Math. J. 13 (1961), 251-264.
• Kashpirovskii, A. I., Equality of the spaces \(S_{\alpha}^{\beta}\) and \(S_{\alpha}\cap S^{\beta}\), (English. Russian original) Funct. Anal. Appl. 14, 129 (1980); translation from Funkts. Anal. Prilozh. 14, No.2,
• 60 (1980).
• Karunakaran, V., Kalpakam, N. V., Boehmians and Fourier transform, Integral Transform. Spec. Funct. 9 (3) (2000), 197-216.
• Mikusiński, P., Convergence of Boehmians, Japan J. Math. 9 (1983), 159-179.
• Mikusiński, P., Boehmians and generalized functions, Acta. Math. Hung. 51 (1988), 271-281.
• Zemanian, A. H., Distribution Theory and Transform Analysis, McGraw-Hill Book Co., New York, 1965.

Identyfikatory

DOI

10.17951/a.2010.54.1.27-43