On the Commutation Properties of Finite Convolution and Differential Operators I: Commutation.

@inproceedings{Grabovsky2021OnTC,
  title={On the Commutation Properties of Finite Convolution and Differential Operators I: Commutation.},
  author={Y. Grabovsky and Narek Hovsepyan},
  year={2021}
}
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. 
1 Citations
On the Commutation Properties of Finite Convolution and Differential Operators II: Sesquicommutation
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 hasExpand

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