The use of the Kontorovich-Lebedev transform in an analysis of regularized Schrodinger equation

In this paper, we introduce a notion of the Schrodinger kernel associated with the familiar KontorovichLebedev transform. In order to control its singularity at infinity, we need to implement the so-called regularization procedure. Hence, we obtain a sequence of regularized kernels which converge to the original kernel when a regularization parameter tends to zero. We study differential properties of the regularized kernel and a solution for a certain type of regularized Schrodinger equation. A family of regularized Weierstrass's transforms is presented. Finally, we examine a pointwise convergence of this sequence of operators, when the regularization parameter tends to zero.