On the solution \(n\)-dimensional of the product \(\otimes k\) operator and diamond Bessel operator (Q980614)

The authors study the equations \(\otimes^k{}\diamondsuit^k{}_B u(x)=f(x)\) and \(\otimes^k{}\diamondsuit^k{}_B u(x)=f(x,\square^{k-1}L^k\Delta^k_B{}\square^{k}_Bu(x))\), where \(u(x)\) is an unknown function of \(x\in \mathbb{R}^n\), \(f(x)\) is a generalized function, and \(k\in \mathbb{N}\). Here, \(\square\) is the usual ultrahyperbolic operator; \[ \otimes=\frac{3}{4}\diamondsuit\Delta+\frac{1}{4}\square^3, \] where \(\Delta\) denotes the usual Laplacian and \(\diamondsuit=\Delta\square\); \[ L= \frac{3}{4}\Delta^2+\frac{1}{4}\square^2; \] \(\square_B\) is the ultrahyperbolic Bessel operator; \(\Delta_B\) is the \(n\)-dimensional Bessel operator; and \(\diamondsuit_B=\Delta_B\square_B\) is the diamond Bessel operator.