Geodesic
Smoothness of Generalized Eigenfunctions of Differential–Difference Operators on a Finite Interval
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 679-701 Cet article a éte moissonné depuis la source Math-Net.Ru

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The eigenfunction–eigenvalue problem for differential–difference operators is considered. Necessary and sufficient conditions for preserving the smoothness of generalized eigenfunctions over the entire interval are obtained. An example is given of a differential–difference operator having a countable set of eigenfunctions whose smoothness is violated inside the interval and a countable set of eigenfunctions whose smoothness is preserved.
Keywords: differential–difference equation, generalized eigenfunction, smoothness. 
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R. Yu. Vorotnikov; A. L. Skubachevskii. Smoothness of Generalized Eigenfunctions of Differential–Difference Operators on a Finite Interval. Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 679-701. http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a3/

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