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

Yurii Luchko; Virginia Kiryakova

Banach Center Publications (2000)

  • Volume: 53, Issue: 1, page 155-165
  • ISSN: 0137-6934

Abstract

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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 ∏ j = 1 m ( x ( d / d x ) + β γ j ) , β>0, γ j ∈ 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.

How to cite

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Luchko, Yurii, and Kiryakova, Virginia. "Hankel type integral transforms connected with the hyper-Bessel differential operators." Banach Center Publications 53.1 (2000): 155-165. <http://eudml.org/doc/209070>.

@article{Luchko2000,
abstract = {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 $B:= x^\{-β\} ∏_\{j=1\}^\{m\} (x(d/dx) + βγ_\{j\})$, β>0, $γ_\{j\} ∈ R$, 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.},
author = {Luchko, Yurii, Kiryakova, Virginia},
journal = {Banach Center Publications},
keywords = {operational relations; generalized Hankel-transform; Meijer's G-function; hyper-Bessel differential operator; Meijer -function; inversion formulas; symmetrical integral transforms of Fourier type; Hankel transform; hyper-Bessel differential operators; Mellin convolution type transforms},
language = {eng},
number = {1},
pages = {155-165},
title = {Hankel type integral transforms connected with the hyper-Bessel differential operators},
url = {http://eudml.org/doc/209070},
volume = {53},
year = {2000},
}

TY - JOUR
AU - Luchko, Yurii
AU - Kiryakova, Virginia
TI - Hankel type integral transforms connected with the hyper-Bessel differential operators
JO - Banach Center Publications
PY - 2000
VL - 53
IS - 1
SP - 155
EP - 165
AB - 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 $B:= x^{-β} ∏_{j=1}^{m} (x(d/dx) + βγ_{j})$, β>0, $γ_{j} ∈ R$, 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.
LA - eng
KW - operational relations; generalized Hankel-transform; Meijer's G-function; hyper-Bessel differential operator; Meijer -function; inversion formulas; symmetrical integral transforms of Fourier type; Hankel transform; hyper-Bessel differential operators; Mellin convolution type transforms
UR - http://eudml.org/doc/209070
ER -

References

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