On the commutation properties of finite convolution and differential operators I: commutation
arXiv:2107.03016
Abstract
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to complex-valued and non self-adjoint operators. In addition, we introduce a new kind of commutation relation, which we call sesquicommutation, that also has implications for the spectral properties of the integral operator. In this case we also compute a complete list of sequicommuting pairs of integral and differential operators.
arXiv admin note: substantial text overlap with arXiv:1807.09252