The solutions of the $n$-dimensional Bessel diamond operator and the Fourier--Bessel transform of their convolution

Simple item page
dc.creatorYildirim, Huseyin
dc.creatorSarikaya, M Zeki
dc.creatorOzturk, Sermin
dc.date2005-03-05
dc.date.accessioned2026-07-07T05:17:41Z
dc.date.available2026-07-07T05:17:41Z
dc.descriptionIn this article, the operator $\Diamond_{B}^{k}$ is introduced and named as the Bessel diamond operator iterated $k$ times and is defined by $ \Diamond_{B}^{k} = [ (B_{x_{1}} + B_{x_{2}} + ... + B_{x_{p}})^{2} - (B_{x_{p + 1}} + ... + B_{x_{p + q}})^{2} ]^{k}$, where $ p + q = n, B_{x_{i}} = \frac{\partial^{2}}{\partial x_{i}^{2}} + \frac{2v_{i}}{x_{i}} \frac{\partial}{\partial x_{i}}, $ where $2v_{i} = 2α_{i} + 1$, $ α_{i} > - {1/2} $ [8], $x_{i} > 0$, $i = 1, 2, ..., n, k$ is a non-negative integer and $n$ is the dimension of $\mathbb{R}_{n}^{+}$. In this work we study the elementary solution of the Bessel diamond operator and the elementary solution of the operator $\Diamond_{B}^{k}$ is called the Bessel diamond kernel of Riesz. Then, we study the Fourier--Bessel transform of the elementary solution and also the Fourier--Bessel transform of their convolution.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0503091
dc.identifierhttp://arxiv.org/abs/math/0503091
dc.identifierProc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 375-387
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74396
dc.subjectAnalysis of PDEs
dc.subject46F10
dc.titleThe solutions of the $n$-dimensional Bessel diamond operator and the Fourier--Bessel transform of their convolution
dc.typetext

Files

Collections

arXiv