Abstract:
In this paper we propose a solution to a certain inverse Sturm-Liouville problem, which allows one to determine the potential and the boundary conditions of the differential operator on the values of one of the differentials of Gateaux zeroes $ x_ {k, n} [q ] \in (0, \pi) $ of some eigenfunction $ \hat y (x, q, \lambda_n [q]) $ for an increment $ w $ from the set $ \mathbb W $. As $ \mathbb W $, we consider some sets of classical and generalized functions.
Keywords:
eigenfunction of Sturm-Liouville problem, nodal points of Sturm-Liouville problem, Gateaux differential, inverse Sturm-Liouville problem, inverse nodal problem, nodal points.
\Bibitem{Try13}
\by A.~Yu.~Trynin
\paper On inverse nodal problem for Sturm-Liouville operator
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 4
\pages 112--124
\mathnet{http://mi.mathnet.ru/eng/ufa227}
\crossref{https://doi.org/10.13108/2013-5-4-112}
\elib{https://elibrary.ru/item.asp?id=20930482}
Linking options:
https://www.mathnet.ru/eng/ufa227
https://doi.org/10.13108/2013-5-4-112
https://www.mathnet.ru/eng/ufa/v5/i4/p116
This publication is cited in the following 14 articles:
A. Yu. Trynin, “Ob odnom metode resheniya smeshannoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s pomoschyu operatorov $\mathbb{AT}_{\lambda,j}$”, Izv. vuzov. Matem., 2024, no. 2, 59–80
V. N. Pasechnik, “Approximation of Continuous Functions by Classical Sincs and Values of Operators Cλ”, Comput. Math. and Math. Phys., 64:2 (2024), 206
A. Yu. Trynin, “On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $\mathbb{A}{{\mathbb{T}}_{{\lambda ,j}}}$”, Russ Math., 68:2 (2024), 52
V. N. Pasechnik, “Priblizhenie nepreryvnykh funktsii s pomoschyu klassicheskikh sinkov i znachenii operatorov Cλ”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:2 (2024), 220
A. Yu. Trynin, “A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$”, Izv. Math., 87:6 (2023), 1227–1254
A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284
A. Yu. Trynin, “Lagrange–Sturm–Liouville Processes”, J Math Sci, 261:3 (2022), 455
A. Yu. Trynin, E. D. Kireeva, “Printsip lokalizatsii na klasse funktsii, integriruemykh po Rimanu, dlya protsessov Lagranzha–Shturma–Liuvillya”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 20:1 (2020), 51–63
A. Yu. Trynin, “Error Estimate for Uniform Approximation by Lagrange–Sturm–Liouville Processes”, J Math Sci, 247:6 (2020), 939
A. Yu. Trynin, “A criterion of convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of variation”, Russian Math. (Iz. VUZ), 62:8 (2018), 51–63
A. Yu. Trynin, “Uniform convergence of Lagrange–Sturm–Liouville processes on one functional class”, Ufa Math. J., 10:2 (2018), 93–108
A. Yu. Trynin, “Sufficient condition for convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of continuity”, Comput. Math. Math. Phys., 58:11 (2018), 1716–1727
A. Yu. Trynin, “Neobkhodimye i dostatochnye usloviya ravnomernoi na otrezke sink-approksimatsii funktsii ogranichennoi variatsii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:3 (2016), 288–298
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