On the commutation properties of finite convolution and differential operators II: sesquicommutation

Yury Grabovsky; Narek Hovsepyan

doi:10.1007/s00025-021-01412-7

paper

On the commutation properties of finite convolution and differential operators II: sesquicommutation

arXiv:1906.02682 · doi:10.1007/s00025-021-01412-7

Abstract

We introduce and fully analyze a new commutation relation $K L_{1} = L_{2} K$ between finite convolution integral operator $K$ and differential operators $L_{1}$ and $L_{2}$ , that has implications for spectral properties of $K$ . This work complements our explicit characterization of commuting pairs $K L = L K$ and provides an exhaustive list of kernels admitting commuting or sesquicommuting differential operators.