On weighted generalized functions associated with quadratic forms

TL;DR

This paper studies weighted generalized functions linked to quadratic forms, focusing on their derivatives and applications in solving ultra-hyperbolic equations with Bessel operators.

Contribution

It introduces new weighted generalized functions associated with quadratic forms and demonstrates their use in constructing solutions for ultra-hyperbolic equations with Bessel operators.

Findings

Construction of fundamental solutions for iterated ultra-hyperbolic equations

Development of negative real powers of ultra-hyperbolic operators

Application of these functions in solving complex differential equations

Abstract

In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with Bessel operator.