On the \(B\)-convolutions of the Bessel diamond kernel of Riesz
type: Item
instance of: scholarly article
title: On the \(B\)-convolutions of the Bessel diamond kernel of Riesz
zbMATH Open document ID: 1162.44003
author: Mehmet Zeki Sarikaya
author: Huseyin Yildirim
published in: Applied Mathematics and Computation
publication date: 2009-03-02T00:00:00Z
review text: Let \(\Delta_B=\sum_{i=1}^nB_{x_i} =\sum_{i=1}^n\Big(\frac{\partial^2}{\partial x_i^2}+\frac{2\nu_i}{x_i}\frac{\partial}{\partial x_i}\Big)\) be the Laplace-Bessel operator and \(\square_B=B_{x_1}+\cdots+B_{x_p}-B_{x_{p+1}}-\cdots-B_{x_{p+q}}\), \(p+q=n\) the ultra-hyperbolic type operator. Then the Bessel diamond operator iterated \(k\)-times \(\diamond_B^k\) is given by \(\square_B^k\Delta_B^k\) and the elementary solution is given by \(T_k=(-1)^kS_{2k}*R_{2k}\), which is called the Bessel diamond kernel of Riesz, where \((-1)^kS_{2k}\) and \(R_{2k}\) are unique elementary solutions \(\Delta_B^k\) and \(\square_B^k\) respectively and \(*\) is the \(B\)-convolution associated to \(\diamond_B^k\). The authors investigate the \(B\)-convolution structure of \(T_k\) as in the classical case of \(\nu_i=0\).
reviewed by: Takeshi Kawazoe
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 35L82
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 5522153
zbMATH Keywords: free group
zbMATH Keywords: Bessel diamond operator
zbMATH Keywords: Bessel diamond kernel
zbMATH Keywords: ultra-hyperbolic type operator
zbMATH Keywords: tempered distribution
zbMATH Keywords: Fourier-Bessel transform
zbMATH Keywords: Bessel transform
zbMATH Keywords: Laplace-Bessel operator
zbMATH Keywords: \(B\)-convolution
MaRDI profile type: Publication
full work available at URL: j.amc.2008.11.014
OpenAlex ID: W2022757999
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DOI: 10.1016/J.AMC.2008.11.014
description: scientific article; zbMATH DE number 5522153