# Weighted spherical means generated by generalized translation and general Euler-Poisson-Darboux equation

## TL;DR

This paper studies weighted spherical means generated by generalized translations and their relation to a generalized Euler-Poisson-Darboux equation, highlighting properties of solutions including the Asgeirsson property in a complex differential operator context.

## Contribution

It introduces a new framework connecting weighted spherical means with a generalized Euler-Poisson-Darboux equation and establishes the Asgeirsson property for solutions involving singular Bessel operators.

## Key findings

- Established the Asgeirsson property for solutions of the ultrahyperbolic equation.
- Connected weighted spherical means with generalized translation and Euler-Poisson-Darboux equations.
- Extended classical results to include singular differential Bessel operators.

## Abstract

We consider the spherical mean generated by a multidimensional generalized translation and general Euler-Poisson-Darboux equation corresponding to this mean. The Asgeirsson property of solutions of the ultrahyperbolic equation that includes singular differential Bessel operators acting by each variable is provided.

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Source: https://tomesphere.com/paper/1703.06340