O. A. Veliev, “Non-Self-Adjoint Sturm–Liouville Operators with Matrix Potentials”, Mat. Zametki, 81:4 (2007), 496–506; Math. Notes, 81:4 (2007), 440

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Matematicheskie Zametki, 2007, Volume 81, Issue 4, Pages 496–506
DOI: https://doi.org/10.4213/mzm3704 (Mi mzm3704)

This article is cited in 15 scientific papers (total in 15 papers)

Non-Self-Adjoint Sturm–Liouville Operators with Matrix Potentials

O. A. Veliev

Dogus University

Full-text PDF (455 kB) Citations (15)

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DOI: https://doi.org/10.4213/mzm3704

Abstract: We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm–Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.

Keywords: Sturm–Liouville operator, non-self-adjoint operator, quasiperiodic boundary condition, Riesz basis, root function, Jordan chain, Bessel operator.

Received: 05.08.2005

English version:
Mathematical Notes, 2007, Volume 81, Issue 4, Pages 440–448
DOI: https://doi.org/10.1134/S0001434607030200

Bibliographic databases:

UDC: 517.953

Language: Russian

Citation: O. A. Veliev, “Non-Self-Adjoint Sturm–Liouville Operators with Matrix Potentials”, Mat. Zametki, 81:4 (2007), 496–506; Math. Notes, 81:4 (2007), 440–448

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Linking options:

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https://doi.org/10.4213/mzm3704

https://www.mathnet.ru/eng/mzm/v81/i4/p496

This publication is cited in the following 15 articles:

Natanael Karjanto, Peter Sadhani, “Unraveling the Complexity of Inverting the Sturm–Liouville Boundary Value Problem to Its Canonical Form”, Mathematics, 12:9 (2024), 1329
Oktay Veliev, “On the bands of the Schrödinger operator with a matrix potential”, Mathematische Nachrichten, 296:3 (2023), 1285
Veliev O.A., “On the Schrodinger Operator With a Periodic Pt-Symmetric Matrix Potential”, J. Math. Phys., 62:10 (2021), 103501
N. P. Bondarenko, “Direct and Inverse Problems for the Matrix Sturm–Liouville Operator with General Self-Adjoint Boundary Conditions”, Math. Notes, 109:3 (2021), 358–378
D. M. Polyakov, “Spectral estimates for the fourth-order operator with matrix coefficients”, Comput. Math. Math. Phys., 60:7 (2020), 1163–1184
D. M. Polyakov, “On the Spectral Characteristics of Non-Self-Adjoint Fourth-Order Operators with Matrix Coefficients”, Math. Notes, 105:4 (2019), 630–635
N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405
Van Gorder R.A., Kim H., Krause A.L., “Diffusive Instabilities and Spatial Patterning From the Coupling of Reaction-Diffusion Processes With Stokes Flow in Complex Domains”, J. Fluid Mech., 877 (2019), 759–823
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
Uskova N.B., “On the spectral properties of a second-order differential operator with a matrix potential”, Differ. Equ., 52:5 (2016), 557–567
F. Seref, O. A. Veliev, “On Sharp Asymptotic Formulas for the Sturm–Liouville Operator with a Matrix Potential”, Math. Notes, 100:2 (2016), 291–297
N. B. Uskova, “On spectral properties of Sturm–Liouville operator with matrix potential”, Ufa Math. J., 7:3 (2015), 84–94
Fulya Şeref, O. A. Veliev, “On non-self-adjoint Sturm-Liouville operators in the space of vector functions”, Math Notes, 95:1-2 (2014), 180
Scherbakov A.O., “Spektralnyi analiz nesamosopryazhennogo operatora Shturma-Liuvillya s singulyarnym potentsialom”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 31:11 (2013), 102–108
Veliev O. A., “Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients”, Bound. Value Probl., 2008, 628973, 22 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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