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Higher order Nevanlinna functions and the inverse three spectra problem

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
he three spectra problem of recovering the Sturm-Liouville equation by the spectrum of the Dirichlet-Dirichlet boundary value problem on [0, α], the Dirichlet-Dirichlet problem on [0, α/2] and the Neumann-Dirichlet problem on [α/2, α] is considered. Sufficient conditions of solvability and of uniqueness of the solution to such a problem are found.
Rocznik
Strony
301--314
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • South-Ukrainian National Pedagogical University Staroportolrankovskaya 26, Odesa, Ukraine, 65020
autor
  • South-Ukrainian National Pedagogical University Staroportolrankovskaya 26, Odesa, Ukraine, 65020
  • South-Ukrainian National Pedagogical University Staroportolrankovskaya 26, Odesa, Ukraine, 65020
Bibliografia
  • [1] O. Boyko, O. Martynyuk, V. Pivovarchik, On a generalization of the three spectral inverse problem, Methods of Functional Analysis and Topology, accepted for publication.
  • [2] O. Boyko, V. Pivovarchik, Ch.-F. Yang, On solvability of the three spectra problem, Mathematische Nachrichten, accepted for publication.
  • [3] M. Drignei, Uniqueness of solutions to inverse Sturm-Liouville problems with L (0,a) potential using three spectra, Advances in Applied Mathematics 42 (2009), 471-482.
  • [4] M. Drignei, Gonstructibility of an L2R(0,a) solution to an inverse Sturm-Liouville using three Dirichlet spectra, Inverse Problems 26 (2010), 025003, 29 pp.
  • [5] S. Fu, Z. Xu, G. Wei, Inverse indefinite Sturm-Liouville problems with three spectra, J. Math. Anal. Appl. 381 (2011), 506-512.
  • [6] F. Gesztesy, B. Simon, Inverse spectral analysis with partial information on the potential, I, the case of discrete spectrum, Trans. Am. Math. Soc. 352 (2000), 2765-2789.
  • [7] O. Hald, Inverse eigenvalue problem for the mantle, Geophys. J. R. Astr. Soc. 62 (1980), 41-48.
  • [8] H. Hochstadt, B. Lieberman, An inverse Sturm-Liouville problems with mixed given data, SIAM J. Appl. Math. 34 (1978), 676-680.
  • [9] R.O. Hryniv, Ya.V. Mykytyuk, Inverse spectral problems for Sturm-Liouville operators with singular potentials. Part III: Reconstruction by three spectra, J. Math. Anal. Appl. 284 (2003) 2, 626-646.
  • [10] I.S. Kac, M.G. Krein, R-functions-analytic functions mapping the upper half-plane into itself Amer. Math. Transl. (2) 103 (1974), 1-18.
  • [11] C.-K. Law, V. Pivovarchik, Characteristic functions of quantum graphs, J. Phys. A: Math. Theor. 42 (2009) 3, 035302, 11 pp.
  • [12] V.A. Marchenko, Sturm-Liouville Operators and Applications, Birkhauser OT 22, Basel, 1986.
  • [13] O. Martynyuk, V. Pivovarchik, On Hochstadt-Lieberman theorem, Inverse Problems 26 (2010) 3, 035011, 6 pp.
  • [14] M. Móller, V. Pivovarchik, Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications, Birkhauser OT, 246, Basel, 2015.
  • [15] V. Pivovarchik, An inverse Sturm-Liouville problem by three spectra, Integral Equations and Operator Theory 34 (1999), 234-243.
  • [16] V. Pivovarchik, Reconstruction of the potential of the Sturm-Liouville equation from, three spectra of boundary value problem, Funct. Anal. Appl. 32 (1999) 3, 87-90.
  • [17] V. Pivovarchik, On Hald-Gesztesy-Simon, Integral Equations and Operator Theory 73 (2012), 383-393.
  • [18] V. Pivovarchik, H. Woracek, Sums of Nevanlinna functions and differential equations on star-shaped graphs, Operators and Matrices 3 (2009) 4, 451-501.
  • [19] L. Sakhnovich, Half-inverse problem, on the finite interva, Inverse Problems 17 (2001), 527-532.
  • [20] T. Suzuki, Inverse problems for heat equations on compact intervals and on circles, I, J. Math. Soc. Japan 38 (1986) 1, 39-65.
  • [21] G. Wei, H.-K. Xu, On the missing eigenvalue problem for an inverse Sturm-Liouville problem, J. Math. Pures Appl. 91 (2009), 468-475.
  • [22] G. Wei, X. Wei, A generalization of three spectra theorem, for inverse Sturm-Liouville problems, Appl. Math. Lett. 35 (2014), 41-45.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bdc3ddf3-1571-4416-be2f-031378b006d5
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