Abstract:
Using the method of similar operators, we study the spectral properties of a fourth-order differential operator with two types of classical boundary conditions. We obtain asymptotics for the spectrum and estimates for the spectral decompositions of this operator. We construct the semigroup generated by the opposite fourth-order differential operator.
Keywords:
fourth-order differential operator, spectrum of operator, method of similar operators.
This publication is cited in the following 18 articles:
Ai-Wei Guan, Chuan-Fu Yang, Natalia P. Bondarenko, “Solving Barcilon's inverse problems by the method of spectral mappings”, Journal of Differential Equations, 416 (2025), 1881
D. M. Polyakov, “On the Spectral Properties of a Fourth-Order Self-Adjoint Operator”, Diff Equat, 59:2 (2023), 168
Dmitry M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math Methods in App Sciences, 46:5 (2023), 5483
Dmitry M. Polyakov, “Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation”, Monatsh Math, 202:1 (2023), 171
Dmitry M. Polyakov, “Eigenvalue Asymptotics and a Trace Formula for a Fourth-Order Differential Operator”, Complex Anal. Oper. Theory, 17:8 (2023)
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “O sglazhivanii operatornogo koeffitsienta differentsialnogo operatora pervogo poryadka v banakhovom prostranstve”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 3–14
D. M. Polyakov, “Spectral estimates for fourth-order differential operator with periodic coefficients”, Russian Math. (Iz. VUZ), 66:7 (2022), 76–81
Dmitry M. Polyakov, “Sharp eigenvalue asymptotics of fourth-order differential operators”, ASY, 130:3-4 (2022), 477
N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405
I. N. Braeutigam, D. M. Polyakov, “On the asymptotics of eigenvalues of a fourth-order differential operator with matrix coefficients”, Differ. Equ., 54:4 (2018), 450–467
N. B. Uskova, G. V. Garkavenko, “The theorem on the decomposition of linear operators and the asymptotic behavior of the eigenvalues of difference operators with a growing potential”, J. Math. Sci., 246:6 (2020), 812–827
A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43
G. V. Garkavenko, N. B. Uskova, “Metod podobnykh operatorov v issledovanii spektralnykh svoistv raznostnykh operatorov s rastuschim potentsialom”, Sib. elektron. matem. izv., 14 (2017), 673–689
G. V. Garkavenko, N. B. Uskova, “Spektralnyi analiz odnogo klassa raznostnykh operatorov s rastuschim potentsialom”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:4 (2016), 395–402
N. B. Uskova, “On the spectral properties of a second-order differential operator with a matrix potential”, Differ. Equ., 52:5 (2016), 557–567
D. M. Polyakov, “Spectral analysis of a fourth order differential operator with periodic and antiperiodic boundary conditions”, St. Petersburg Math. J., 27:5 (2016), 789–811
N. B. Uskova, “On spectral properties of Sturm–Liouville operator with matrix potential”, Ufa Math. J., 7:3 (2015), 84–94
D. Polyakov, A. Zvyagin, “On dissipative solutions of the Jeffreys-Oldroyt-alpha equation”, Advancements in Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020089
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