The reducibility Of An Airy Operator

Abstract

We show that the determinant $\nabla (d,\alpha ),$ which seems to be not considered in the past, is not zero. As an application of this result we prove that the Setoyanagi operator $S_{p,q}={\partial }^2-(a{x}^p+b{x}^q)$ is irreducible over $\mathbb{C}(x)[\partial ]$.

arXiv comment8 pages