Pseudoshift and the Fundamental Solution of the Kipriyanov -Operator.

Solutions of singular differential equations with the Bessel operator of negative order are studied. In this regard, of great interest are the solutions of the singular differential Bessel equation , which are presented in the paper as linearly independent functions and , . Some properties of the functions expressed in terms of the properties of the Bessel–Levitan -function are considered. The direct and inverse -Bessel transforms are introduced, and the -pseudoshift operator that commutes with the Bessel operator is defined. The fundamental solution of the ordinary singular differential operator is found. A representation of the fundamental solution of the Kipriyanov -operator with a singularity at the point and on the cone in the Euclidean -dimensional half-space is given. [ABSTRACT FROM AUTHOR]