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Inverse singular spectral problem via Hocshtadt-Lieberman method

Year 2016, Volume: 65 Issue: 2, 89 - 96, 01.08.2016
https://doi.org/10.1501/Commua1_0000000762

References

  • Freiling, G. Yurko, V.A Inverse Sturm-Liouville Problems and their Applications Nova Sci- ence, New York, 2001.
  • Ambarzumjan V.A., Über eine Erage der Eigenwerttheorie, Z. Phys 53 (1929), 690-695.
  • Borg, G., Eine Umkehrung der Sturm-Liouvillschen Eigenwertaufgabe. Bestimmung der Diğerantial-gleichung durch die Eigenwerte, Acta Math. 78, No: 2 (1945), 1-96.
  • Tikhonov,A. N., On the uniqueness of the solution of the problem of electromagnetic sounding, Dokl. Akad. Nauk SSSR 69 (1949), 797-800.
  • Marchenko V.A. Sturm-Liouville Operators and Applications, Birhkaüser, Basel, 1886.
  • Krein, M.G., Solution of the inverse Sturm-Liouville problem, Dokl. Akad. Nauk SSSR 76 (1951), 21-24.
  • Gel’fand, I.M., and B.M. Levitan, On the determination of a diğerential equation by its spectral function, Izv. Akad. Nauk SSSR Ser. Mat.15, 1951.
  • Hochstadt, H. and Lieberman, B. An Inverse Sturm-Liouville Problem with Mixed Given Data, SIAM J. Appl. Math., V.34, (1978), 676-680 .
  • Gesztesy, F., Simon. B. Inverse Spectral Analysis with Partial Information on the Potential. II: The Case of Discrete Spectrum, Trans. Amer. Math. Soc., V.352, (2000), 2765-2787.
  • Gasımov, Z.M., Inverse problem with two spectra for a singular Sturm-Liouville equation Dokl. RAN, V 365, No:3,(1999), 304-305.
  • Gasımov, Z.M., On the determination of the Singular Sturm Liouville diğerential equation, Academic Congress of Kravchcuk Kiev 1992.
  • Carlson, R. Inverse Spectral Theory for Some Singular Sturm-Liouville problems, Jour. of Dif. Eq., V.106, (1993),121-140.
  • Courant, R. and Hilbert, D. Methods of Mathematical Physics, New York, 1953.
  • Fok, V.A. Beginnings of Quantum Mechanics, Izdat. Leningrad. Gos. Univ., (Russian) (1932).
  • Hald, O.H. Inverse Eigenvalue Problem for the Mantle,Geophys. J.R. Astr. Soc., V.62, (1980), 48.
  • Hryniv, O.R., Mykytyuk, Y.V. Half-Inverse Spectral Problems for Sturm-Liouville Operators with Singular Potentials, Inverse Problems, V.20, N.5, 2004,1423-1444.
  • Koyunbakan H., Panakhov, E.S. Half Inverse Problem for Singular Diğerential Operator, Appl. Analysis, V.84, N.3, 2005, 247-252.
  • Levitan, B.M., Sargsyan, I.S. Introduction to Spectral Theory, Nauka, Moskow, 1970.
  • Malamud, M.M. Uniqueness Questions in Inverse Problems for Systems of Diğerential Equa- tions on a Finite Interval, Trans. Moscow Math. Soc., V.60, (1999), 204-262.
  • Sakhnovich, L. Half-Inverse Problems on the Finite Interval, Inverse Problems, V.17, (2001), 532.
  • Panakhov., E. S. and Yilmazer, R. “A Hochstadt–Lieberman theorem for hydrogen atom equation,” Int. J. Appl. Comput. Math., 11. (2012), 74-80.
  • Bairamov, E., Çakar, Ö., Krall A. M. An Eigenfunction Expansion for a Quadratic Pencil of a Schrödinger Operator with Spectral Singularities, J. of Diğerential Equations, V. 151- ,(1999), 268-289.
  • Bairamov, E., Aygar, Y., Koprubasi, T. The spectrum of eigenparameter-dependent discrete Sturm–Liouville equations, J. of Comp. and Appl. Math. V. 235-16, (2011), 4519-4523.
  • Gasımov, Z.M., Solved Inverse Problems for Singular Sturm Liouville Diğerential Equation from two spectra, Baku State University. Phd, thesis, 1992.
  • Volk, V.Y. On Inverse Formulas for a Diğerential Equation with a Singularity at . Usp. Mat. Nauk (N.S), V.56, N.8, (1953),141-151.
  • Carothers, N.L., Real Analysis Cambridge University, Newyork, 2000.
  • Current address : Department of Mathematics, Firat University, 23119 Elazig/Turkey
  • E-mail address : erdalmat@yahoo.com
Year 2016, Volume: 65 Issue: 2, 89 - 96, 01.08.2016
https://doi.org/10.1501/Commua1_0000000762

References

  • Freiling, G. Yurko, V.A Inverse Sturm-Liouville Problems and their Applications Nova Sci- ence, New York, 2001.
  • Ambarzumjan V.A., Über eine Erage der Eigenwerttheorie, Z. Phys 53 (1929), 690-695.
  • Borg, G., Eine Umkehrung der Sturm-Liouvillschen Eigenwertaufgabe. Bestimmung der Diğerantial-gleichung durch die Eigenwerte, Acta Math. 78, No: 2 (1945), 1-96.
  • Tikhonov,A. N., On the uniqueness of the solution of the problem of electromagnetic sounding, Dokl. Akad. Nauk SSSR 69 (1949), 797-800.
  • Marchenko V.A. Sturm-Liouville Operators and Applications, Birhkaüser, Basel, 1886.
  • Krein, M.G., Solution of the inverse Sturm-Liouville problem, Dokl. Akad. Nauk SSSR 76 (1951), 21-24.
  • Gel’fand, I.M., and B.M. Levitan, On the determination of a diğerential equation by its spectral function, Izv. Akad. Nauk SSSR Ser. Mat.15, 1951.
  • Hochstadt, H. and Lieberman, B. An Inverse Sturm-Liouville Problem with Mixed Given Data, SIAM J. Appl. Math., V.34, (1978), 676-680 .
  • Gesztesy, F., Simon. B. Inverse Spectral Analysis with Partial Information on the Potential. II: The Case of Discrete Spectrum, Trans. Amer. Math. Soc., V.352, (2000), 2765-2787.
  • Gasımov, Z.M., Inverse problem with two spectra for a singular Sturm-Liouville equation Dokl. RAN, V 365, No:3,(1999), 304-305.
  • Gasımov, Z.M., On the determination of the Singular Sturm Liouville diğerential equation, Academic Congress of Kravchcuk Kiev 1992.
  • Carlson, R. Inverse Spectral Theory for Some Singular Sturm-Liouville problems, Jour. of Dif. Eq., V.106, (1993),121-140.
  • Courant, R. and Hilbert, D. Methods of Mathematical Physics, New York, 1953.
  • Fok, V.A. Beginnings of Quantum Mechanics, Izdat. Leningrad. Gos. Univ., (Russian) (1932).
  • Hald, O.H. Inverse Eigenvalue Problem for the Mantle,Geophys. J.R. Astr. Soc., V.62, (1980), 48.
  • Hryniv, O.R., Mykytyuk, Y.V. Half-Inverse Spectral Problems for Sturm-Liouville Operators with Singular Potentials, Inverse Problems, V.20, N.5, 2004,1423-1444.
  • Koyunbakan H., Panakhov, E.S. Half Inverse Problem for Singular Diğerential Operator, Appl. Analysis, V.84, N.3, 2005, 247-252.
  • Levitan, B.M., Sargsyan, I.S. Introduction to Spectral Theory, Nauka, Moskow, 1970.
  • Malamud, M.M. Uniqueness Questions in Inverse Problems for Systems of Diğerential Equa- tions on a Finite Interval, Trans. Moscow Math. Soc., V.60, (1999), 204-262.
  • Sakhnovich, L. Half-Inverse Problems on the Finite Interval, Inverse Problems, V.17, (2001), 532.
  • Panakhov., E. S. and Yilmazer, R. “A Hochstadt–Lieberman theorem for hydrogen atom equation,” Int. J. Appl. Comput. Math., 11. (2012), 74-80.
  • Bairamov, E., Çakar, Ö., Krall A. M. An Eigenfunction Expansion for a Quadratic Pencil of a Schrödinger Operator with Spectral Singularities, J. of Diğerential Equations, V. 151- ,(1999), 268-289.
  • Bairamov, E., Aygar, Y., Koprubasi, T. The spectrum of eigenparameter-dependent discrete Sturm–Liouville equations, J. of Comp. and Appl. Math. V. 235-16, (2011), 4519-4523.
  • Gasımov, Z.M., Solved Inverse Problems for Singular Sturm Liouville Diğerential Equation from two spectra, Baku State University. Phd, thesis, 1992.
  • Volk, V.Y. On Inverse Formulas for a Diğerential Equation with a Singularity at . Usp. Mat. Nauk (N.S), V.56, N.8, (1953),141-151.
  • Carothers, N.L., Real Analysis Cambridge University, Newyork, 2000.
  • Current address : Department of Mathematics, Firat University, 23119 Elazig/Turkey
  • E-mail address : erdalmat@yahoo.com
There are 28 citations in total.

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Primary Language English
Journal Section Research Articles
Authors

Erdal Bas This is me

Publication Date August 1, 2016
Published in Issue Year 2016 Volume: 65 Issue: 2

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APA Bas, E. (2016). Inverse singular spectral problem via Hocshtadt-Lieberman method. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 89-96. https://doi.org/10.1501/Commua1_0000000762
AMA Bas E. Inverse singular spectral problem via Hocshtadt-Lieberman method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2016;65(2):89-96. doi:10.1501/Commua1_0000000762
Chicago Bas, Erdal. “Inverse Singular Spectral Problem via Hocshtadt-Lieberman Method”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 2 (August 2016): 89-96. https://doi.org/10.1501/Commua1_0000000762.
EndNote Bas E (August 1, 2016) Inverse singular spectral problem via Hocshtadt-Lieberman method. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 2 89–96.
IEEE E. Bas, “Inverse singular spectral problem via Hocshtadt-Lieberman method”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 2, pp. 89–96, 2016, doi: 10.1501/Commua1_0000000762.
ISNAD Bas, Erdal. “Inverse Singular Spectral Problem via Hocshtadt-Lieberman Method”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/2 (August 2016), 89-96. https://doi.org/10.1501/Commua1_0000000762.
JAMA Bas E. Inverse singular spectral problem via Hocshtadt-Lieberman method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:89–96.
MLA Bas, Erdal. “Inverse Singular Spectral Problem via Hocshtadt-Lieberman Method”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 2, 2016, pp. 89-96, doi:10.1501/Commua1_0000000762.
Vancouver Bas E. Inverse singular spectral problem via Hocshtadt-Lieberman method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(2):89-96.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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