Hankel type integral transforms connected with the hyper-Bessel differential operators

Luchko, Yurii; Kiryakova, Virginia

Banach Center Publications, Tome 51 (2000), p. 155-165 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we give a solution of a problem posed by the second author in her book, namely, to find symmetrical integral transforms of Fourier type, generalizing the cos-Fourier (sin-Fourier) transform and the Hankel transform, and suitable for dealing with the hyper-Bessel differential operators of order m>1 $B : = x^{- β} \prod_{j = 1}^{m} (x (d / d x) + β γ_{j})$ , β>0, $γ_{j} \in R$ , j=1,...,m. We obtain such integral transforms corresponding to hyper-Bessel operators of even order 2m and belonging to the class of the Mellin convolution type transforms with the Meijer G-function as kernels. Inversion formulas and some operational relations for these transforms are found.

Publié le : 2000-01-01

Zbl 0963.44004

EUDML-ID : urn:eudml:doc:209070

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     author = {Luchko, Yurii and Kiryakova, Virginia},
     title = {Hankel type integral transforms connected with the hyper-Bessel differential operators},
     journal = {Banach Center Publications},
     volume = {51},
     year = {2000},
     pages = {155-165},
     zbl = {0963.44004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv53z1p155bwm}
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Luchko, Yurii; Kiryakova, Virginia. Hankel type integral transforms connected with the hyper-Bessel differential operators. Banach Center Publications, Tome 51 (2000) pp. 155-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv53z1p155bwm/

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