Integral transformations by the index of Lommel's function
type: Item
instance of: scholarly article
title: Integral transformations by the index of Lommel's function
zbMATH Open document ID: 1052.44002
DOI: 10.1023/A:1025948428875
published in: Periodica Mathematica Hungarica
publication date: 2004-09-07T00:00:00Z
review text: Given the integral operator \[ (S_\mu f) (x)=2^{1-\mu}\int^\infty_0 f(\tau)\left| \Gamma\left( \frac{1-\mu+i\tau}{2}\right)\right| ^2 S_{\mu,i\tau}(x) \,d\tau,\;x>0,\;\mu\in \mathbb R,\;| \mu| <1, \] where \(f\) belongs to the Lebesgue space of summable functions, \(\Gamma(z)\) is the Euler gamma-function, \(S_{\mu,i\tau}(x)\) is the kernel Lommel function (a special Bessel type function), where \(\mu\) is a fixed number, one studies its boundedness and inversion properties by using the methods of Fourier, Laplace and Kontorovich-Lebedev transforms theory. An inversion formula is finally proved.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 2099015
zbMATH Keywords: Lommel functions
zbMATH Keywords: Macdonald function
zbMATH Keywords: Mellin transform
zbMATH Keywords: Laplace transform
zbMATH Keywords: Kontorovich-Lebedev transform
zbMATH Keywords: Parseval equality
zbMATH Keywords: boundedness
zbMATH Keywords: inversion formula
author: S. Yakubovich
MaRDI profile type: Publication
cites work: Q5820721
cites work: Q3999257
cites work: Q5846853
cites work: Q4841241
cites work: Index integral transformations of Titchmarsh type
cites work: Index transforms associated with Bessel and Lommel functions
full work available at URL: a:1025948428875
OpenAlex ID: W1762123025
description: scientific article; zbMATH DE number 2099015