Geodesic
Smoothness of Generalized Eigenfunctions of Differential--Difference Operators on a Finite Interval
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 679-701

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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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     author = {R. Yu. Vorotnikov and A. L. Skubachevskii},
     title = {Smoothness of {Generalized} {Eigenfunctions} of {Differential--Difference} {Operators} on a {Finite} {Interval}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {5},
     year = {2023},
     language = {ru},
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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/