The Transmutation Operators and Corresponding Hyperbolic Equations

TL;DR

This paper investigates the conditions under which transmutation operators exist for second-order differential operators and explicitly constructs hyperbolic equations and solutions that define these operators.

Contribution

It provides explicit forms of hyperbolic equations and solutions for constructing transmutation operators for arbitrary second-order differential operators.

Findings

Existence conditions for transmutation operators established

Explicit hyperbolic equations derived for operator kernels

Solutions provided for constructing transmutation operators

Abstract

For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their solutions leading to the kernels of the transmutation operators.