Boehmians of type S and their Fourier transforms
R. Bhuvaneswari ; V. Karunakaran
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 54 (2010), / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:289830 
@article{bwmeta1.element.ojs-doi-10_17951_a_2010_54_1_27-43,
     author = {R. Bhuvaneswari and V. Karunakaran},
     title = {Boehmians of type S and their Fourier transforms},
     journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
     volume = {54},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2010_54_1_27-43}
}

R. Bhuvaneswari; V. Karunakaran. Boehmians of type S and their Fourier transforms. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 54 (2010) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2010_54_1_27-43/

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 Sαβ and Sα∩Sβ, (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.