Generalized solutions of the degenerate hyperbolic equation of the second kind with a spectral parameter

TL;DR

This paper investigates generalized solutions for a degenerate hyperbolic equation of the second kind with a spectral parameter, introducing new operators with Bessel functions to explicitly solve associated problems.

Contribution

It introduces a new class of generalized solutions and operators involving Bessel functions for degenerate hyperbolic equations with spectral parameters.

Findings

Explicit representations of solutions are obtained.

Operators with Bessel functions are characterized and utilized.

The importance of generalized solution classes is demonstrated.

Abstract

For a degenerate hyperbolic equation of the second kind, and with a spectral parameter are studied the Cauchy problem, Cauchy-Goursat and Goursat in a new class of generalized solutions and is given an example that shows the importance of introducing the concept of such a class. Some operators with Bessel functions in the nucleus are introduced and their basic properties are studied. The important identities of these operators are helped to find an explicit representations of the stated problems.