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On the Invertibility Conditions of Finite-Difference Operators

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Abstract

The invertibility of second-order finite-difference operators with constant operator coefficients acting in the Banach space of two-sided vector sequences is proved under the condition of their uniform injectivity (in particular, left invertibility), or surjectivity (in particular, right invertibility), or the Fredholm property.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    L. Yu. Kabantsova

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  1. L. Yu. Kabantsova
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Correspondence to L. Yu. Kabantsova.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 171, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 2, 2019.

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Kabantsova, L.Y. On the Invertibility Conditions of Finite-Difference Operators. J Math Sci 263, 691–697 (2022). https://doi.org/10.1007/s10958-022-05959-w

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  • DOI: https://doi.org/10.1007/s10958-022-05959-w

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