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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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/

[1] G. A. Kamenskii, A. D. Myshkis, “K postanovke kraevykh zadach dlya differentsialnykh uravnenii s otklonyayuschimsya argumentom i neskolkimi starshimi chlenami”, Differents. uravneniya, 10:3 (1974), 409–418 | MR | Zbl

[2] A. G. Kamenskii, “Kraevye zadachi dlya uravnenii s formalno simmetrichnymi differentsialno-raznostnymi operatorami”, Differents. uravneniya, 12:5 (1976), 815–824 | MR

[3] N. N. Krasovskii, Teoriya upravleniya dvizheniem. Lineinye sistemy, Nauka, M., 1968 | MR

[4] Yu. S. Osipov, “O stabilizatsii upravlyaemykh sistem s zapazdyvaniem”, Differents. uravneniya, 1:5 (1965), 605–618 | MR | Zbl

[5] A. V. Kryazhimskii, V. I. Maksimov, Yu. S. Osipov, “O pozitsionnom modelirovanii v dinamicheskikh sistemakh”, Prikl. mat. mekh., 47:6 (1983), 883–890 | MR

[6] G. A. Kamenskii, A. D. Myshkis, A. L. Skubachevskii, “O gladkikh resheniyakh kraevoi zadachi dlya differentsialno-raznostnogo uravneniya neitralnogo tipa”, Ukr. matem. zhurn., 37:5 (1985), 581–585 | MR

[7] A. L. Skubachevskii, Elliptic Functional-Differential Equations and Applications, Oper. Theory Adv. Appl., 91, Birkhäuser, Basel–Boston–Berlin, 1997 | MR

[8] A. L. Skubachevskii, N. O. Ivanov, “Ob obobschennykh resheniyakh vtoroi kraevoi zadachi dlya differentsialno-raznostnykh uravnenii s peremennymi koeffitsientami”, Posvyaschaetsya 70-letiyu prezidenta RUDN V. M. Filippova, SMFN, 67, RUDN, M., 2021, 576–595 | DOI

[9] A. L. Skubachevskii, N. O. Ivanov, “Vtoraya kraevaya zadacha dlya differentsialno-raznostnykh uravnenii”, Dokl. RAN. Matem., inform., prots. upr., 500 (2021), 74–77 | DOI | Zbl

[10] A. L. Skubachevskii, N. O. Ivanov, “Ob obobschennykh resheniyakh vtoroi kraevoi zadachi dlya differentsialno-raznostnykh uravnenii s peremennymi koeffitsientami na intervale netseloi dliny”, Matem. zametki, 111:6 (2022), 873–886 | DOI

[11] D. A. Neverova, A. L. Skubachevskii, “O klassicheskikh i obobschennykh resheniyakh kraevykh zadach dlya differentsialno-raznostnykh uravnenii s peremennymi koeffitsientami”, Matem. zametki, 94:5 (2013), 702–719 | DOI | MR | Zbl

[12] D. A. Neverova, A. L. Skubachevskii, “Klassicheskie resheniya kraevykh zadach dlya differentsialno-raznostnykh uravnenii”, Differents. uravneniya, 49:3 (2013), 300–309 | MR

[13] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[14] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1988 | MR