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On the Commutation Properties of Finite Convolution and Differential Operators II: Sesquicommutation

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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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References

  1. Grabovsky, Y., Hovsepyan, N.: On the commutation properties of finite convolution and differential operators I: commutation (preprint)

  2. Grunbaum, F.A.: Differential operators commuting with convolution integral operators. J. Math. Anal. Appl. 91(1), 80–93 (1983)

    Article  MathSciNet  Google Scholar 

  3. Morrison, J.A.: On the commutation of finite integral operators, with difference kernels, and linear self-adjoint differential operators. Not. Am. Math. Soc. 9, 119 (1962)

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  4. Widom, H.: Asymptotic behavior of the eigenvalues of certain integral equations II. Arch. Rat. Mech. Anal. 17, 215–229 (1964)

    Article  MathSciNet  Google Scholar 

  5. Wright, P.E.: Finite symmetric convolution operators and singular symmetric differential operators. J. Math. Anal. Appl. 148(2), 538–547 (1990)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1714287.

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  1. Temple University, Philadelphia, USA

    Yury Grabovsky & Narek Hovsepyan

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  1. Yury Grabovsky
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  2. Narek Hovsepyan
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Correspondence to Narek Hovsepyan.

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Grabovsky, Y., Hovsepyan, N. On the Commutation Properties of Finite Convolution and Differential Operators II: Sesquicommutation. Results Math 76, 111 (2021). https://doi.org/10.1007/s00025-021-01412-7

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  • DOI: https://doi.org/10.1007/s00025-021-01412-7

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