English

On the commutation properties of finite convolution and differential operators I: commutation

Classical Analysis and ODEs 2021-07-08 v1

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.

Keywords

Cite

@article{arxiv.2107.03016,
  title  = {On the commutation properties of finite convolution and differential operators I: commutation},
  author = {Yury Grabovsky and Narek Hovsepyan},
  journal= {arXiv preprint arXiv:2107.03016},
  year   = {2021}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1807.09252

R2 v1 2026-06-24T03:57:20.378Z