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arXiv · 2107.03016

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

Yury Grabovsky·Narek Hovsepyan
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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.

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Yury Grabovsky, Narek Hovsepyan. 2021-07-07. On the commutation properties of finite convolution and differential operators I: commutation. https://arxiv.org/abs/2107.03016

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