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arXiv · 1906.02682

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

Yury Grabovsky·Narek Hovsepyan
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Abstract

We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ 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 $KL=LK$ and provides an exhaustive list of kernels admitting commuting or sesquicommuting differential operators.

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Yury Grabovsky, Narek Hovsepyan. 2019-06-04. On the commutation properties of finite convolution and differential operators II: sesquicommutation. https://doi.org/10.1007/s00025-021-01412-7

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