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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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
Keywords and phrases
- second-order finite-difference operator
- uniform injectivity
- surjectivity
- Fredholm property
- spectrum
- invertibility