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arXiv · 1807.09252

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

Yury Grabovsky·Narek Hovsepyan
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Abstract

The commutation relation $KL = LK$ between finite convolution integral operator $K$ and differential operator $L$ has implications for spectral properties of $K$. We characterize all operators $K$ admitting this commutation relation. Our analysis places no symmetry constraints on the kernel of $K$ extending the well-known results of Morrison for real self-adjoint finite convolution integral operators.

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Yury Grabovsky, Narek Hovsepyan. 2018-07-24. On the commutation properties of finite convolution and differential operators I: commutation. https://doi.org/10.1007/s00025-021-01411-8

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