# Poisson and heat semigroups for Bessel operator and on the hyperbolic space

## TL;DR

This paper derives explicit formulas for Poisson and heat semigroups related to the Bessel operator and hyperbolic spaces, enhancing understanding of their mathematical properties and potential applications.

## Contribution

It provides new explicit formulas for semigroups associated with the Bessel operator and hyperbolic spaces, which were previously not fully characterized.

## Key findings

- Explicit formulas for Poisson semigroup on hyperbolic space
- Explicit formulas for heat semigroup on hyperbolic space
- Enhanced mathematical understanding of Bessel operator semigroups

## Abstract

In this paper we find explicit formulas for the Poisson and heat semigroups associated to the modified Bessel operator and on the hyperbolic spaces $\mathbb{H}^n$.