An integral formula for L^2-eigenfunctions of a fourth order Bessel-type differential operator

TL;DR

This paper derives an explicit integral formula for eigenfunctions of a fourth order Bessel-type differential operator, linking two models of the minimal representation of an indefinite orthogonal group.

Contribution

It provides a new integral representation for eigenfunctions, connecting L^2 and conformal models of the minimal representation.

Findings

Explicit integral formula for eigenfunctions

Connection between L^2 and conformal models

Advancement in understanding Bessel-type operators

Abstract

We find an explicit integral formula for the eigenfunctions of a fourth order differential operator against the kernel involving two Bessel functions. Our formula establishes the relation between K-types in two different realizations of the minimal representation of the indefinite orthogonal group, namely the L^2-model and the conformal model.