An integral representation of eigenfunctions for the deformed Noumi--Sano operators

Abstract

The deformed Noumi-Sano operator $H_{n, m}^d(x, y)$ of order $d$ is a simultaneous extension of the Macdonald operator and the Noumi-Sano operator. In this paper, we construct an integral transform associated with eigenvalue problem of $H_{n, m}^d(x, y)$. Using the integral transform, we obtain an integral representation of eigenfunctions for $H_{n, m}^d(x, y)$.