English

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

Analysis of PDEs 2021-06-04 v1 Classical Analysis and ODEs

Abstract

We introduce and fully analyze a new commutation relation KL1=L2K\overline{K} L_1 = L_2 K between finite convolution integral operator KK and differential operators L1L_1 and L2L_{2}, that has implications for spectral properties of KK. This work complements our explicit characterization of commuting pairs KL=LKKL=LK and provides an exhaustive list of kernels admitting commuting or sesquicommuting differential operators.

Keywords

Cite

@article{arxiv.1906.02682,
  title  = {On the commutation properties of finite convolution and differential operators II: sesquicommutation},
  author = {Yury Grabovsky and Narek Hovsepyan},
  journal= {arXiv preprint arXiv:1906.02682},
  year   = {2021}
}