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

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

2005-03-05

arxiv.org/abs/math/0503091v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 375-387

Mathematics

Analysis of PDEs

13 pages

Scientific paper

In 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 $2v_{i} = 2\alpha_{i} + 1$, $ \alpha_{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.

Affiliated with

Also associated with

No associations

Rating

The solutions of the $n$-dimensional Bessel diamond operator and the Fourier--Bessel transform of their convolution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The solutions of the $n$-dimensional Bessel diamond operator and the Fourier--Bessel transform of their convolution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The solutions of the $n$-dimensional Bessel diamond operator and the Fourier--Bessel transform of their convolution will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-257139