On the solution of nn-dimensional and the Fourier Bessel transform of the operator ⊗Bk

In this paper, we consider the solution of equation ⊗Bku(x)=∑r=0mcr⊗Brδ where ⊗Bk is the otimes operator iterated kk times and is defined by ⊗Bk=((∑i=1pBxi)3−(∑j=p+1p+qBxi)3)k, where p+q=n,Bxi=∂2∂xi2+2vixi∂∂xi, 2vi=2αi+1,αi>−12, i=1,2,3,…,ni=1,2,3,…,n and nn is the dimension of the Rn+, and k=0,1,2,3,…,crk=0,1,2,3,…,cr is a constant. It was found that the type of the solution of this equation, such as the ordinary functions, the tempered distributions and the singular distributions, depend on the relationship between the values of kk and mm. After that we study the Fourier Bessel transform of the elementary solution of the operator ⊗Bk and also the Fourier Bessel transform of their convolution.