We study various direct and inverse spectral problems for the one-dimensional Schrödinger equation with distributional potential and boundary conditions containing the eigenvalue parameter.
REFERENCES
1.
S.
Albeverio
, P.
Binding
, R.
Hryniv
, and Ya.
Mykytyuk
, “Inverse spectral problems for coupled oscillating systems
,” Inverse Probl.
23
(3
), 1181
–1200
(2007
).2.
S.
Albeverio
, F.
Gesztesy
, R.
Høegh-Krohn
, and H.
Holden
, Solvable Models in Quantum Mechanics
(AMS Chelsea Publishing
, Providence, RI
, 2005
).3.
S.
Albeverio
and P.
Kurasov
, Singular Perturbations of Differential Operators: Solvable Schrödinger Type Operators
(Cambridge University Press
, Cambridge
, 2000
).4.
R. Kh.
Amirov
, A. S.
Ozkan
, and B.
Keskin
, “Inverse problems for impulsive Sturm–Liouville operator with spectral parameter linearly contained in boundary conditions
,” Integral Transforms Spec. Funct.
20
(7-8
), 607
–618
(2009
).5.
P. A.
Binding
, P. J.
Browne
, and B. A.
Watson
, “Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. I
,” Proc. Edinburgh Math. Soc.(2)
45
(3
), 631
–645
(2002
).6.
P. A.
Binding
, P. J.
Browne
, and B. A.
Watson
, “Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. II
,” J. Comput. Appl. Math.
148
(1
), 147
–168
(2002
).7.
J.
Eckhardt
, F.
Gesztesy
, R.
Nichols
, and G.
Teschl
, “Weyl–Titchmarsh theory for Sturm–Liouville operators with distributional potentials
,” Opuscula Math.
33
(3
), 467
–563
(2013
); e-print arXiv:1208.4677.8.
J.
Eckhardt
, F.
Gesztesy
, R.
Nichols
, and G.
Teschl
, “Inverse spectral theory for Sturm–Liouville operators with distributional potentials
,” J. London Math. Soc. (2)
88
(3
), 801
–828
(2013
); e-print arXiv:1210.7628.9.
G.
Freiling
and V.
Yurko
, “Inverse problems for Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter
,” Inverse Probl.
26
(5
), 055003
(2010
).10.
C. T.
Fulton
, “Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
,” Proc. R. Soc. Edinburgh, Sect. A
77
(3-4
), 293
–308
(1977
).11.
C. T.
Fulton
, “Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions
,” Proc. R. Soc. Edinburgh, Sect. A
87
(1-2
), 1
–34
(1980
).12.
A.
Goriunov
and V.
Mikhailets
, “Regularization of singular Sturm–Liouville equations
,” Methods Funct. Anal. Topol.
16
(2
), 120
–130
(2010
); e-print arXiv:1002.4371.13.
N. J.
Guliyev
, “Inverse eigenvalue problems for Sturm–Liouville equations with spectral parameter linearly contained in one of the boundary conditions
,” Inverse Probl.
21
(4
), 1315
–1330
(2005
); e-print arXiv:0803.0566.14.
N. J.
Guliyev
, “Essentially isospectral transformations and their applications
,” preprint arXiv:1708.07497.15.
16.
N. J.
Guliyev
, “On extensions of symmetric operators
,” Oper. Matrices
(to be published); e-print arXiv:1807.11865.17.
M.
Homa
and R.
Hryniv
, “Comparison and oscillation theorems for singular Sturm–Liouville operators
,” Opusc. Math.
34
(1
), 97
–113
(2014
).18.
R. O.
Hryniv
and Ya. V.
Mykytyuk
, “Inverse spectral problems for Sturm–Liouville operators with singular potentials
,” Inverse Probl.
19
(3
), 665
–684
(2003
); e-print arXiv:math/0211247.19.
R. O.
Hryniv
and Ya. V.
Mykytyuk
, “Inverse spectral problems for Sturm–Liouville operators with singular potentials. II. Reconstruction by two spectra
,” in Functional Analysis and Its Applications
(Elsevier
, Amsterdam
, 2004
), pp. 97
–114
; e-print arXiv:math/0301193.20.
R. O.
Hryniv
and Ya. V.
Mykytyuk
, “Half-inverse spectral problems for Sturm–Liouville operators with singular potentials
,” Inverse Probl.
20
(5
), 1423
–1444
(2004
); e-print arXiv:math/0312184.21.
Ch. G.
Ibadzadeh
and I. M.
Nabiev
, “Reconstruction of the Sturm–Liouville operator with nonseparated boundary conditions and a spectral parameter in the boundary condition
,” Ukraïn. Mat. Z.
69
(9
), 1217
–1223
(2017
) (in Russian)Ch. G.
Ibadzadeh
and I. M.
Nabiev
, [Ukrainian Math. J.
69
(9
), 1416
–1423
(2018
) (in English)].22.
A.
Kostenko
and M.
Malamud
, “1-D Schrödinger operators with local point interactions: A review
,” in Spectral Analysis, Differential Equations and Mathematical Physics
(American Mathematical Society
, Providence, RI
, 2013
), pp. 235
–262
; e-print arXiv:1303.4055.23.
N. Dzh.
Kuliev
, “Inverse problems for the Sturm–Liouville equation with a spectral parameter in the boundary condition
,” Dokl. Nats. Akad. Nauk Azerb.
60
(3-4
), 10
–16
(2004
) (in Russian).24.
Kh. R.
Mamedov
and F. A.
Cetinkaya
, “Eigenparameter dependent inverse boundary value problem for a class of Sturm–Liouville operator
,” Bound. Value Probl.
2014
, 194
.25.
K. A.
Mirzoev
, “Sturm–Liouville operators
,” Tr. Mosk. Mat. Obs.
75
(2
), 335
–359
(2014
) (in Russian)K. A.
Mirzoev
, [Trans. Moscow Math. Soc.
75
, 281
–299
(2014
) (in English)].26.
A. M.
Savchuk
, “On the eigenvalues and eigenfunctions of the Sturm–Liouville operator with a singular potential
,” Mat. Zametki
69
(2
), 277
–285
(2001
) (in Russian)A. M.
Savchuk
, [Math. Notes
69
(1-2
), 245
–252
(2001
) (in English)].27.
A. M.
Savchuk
and A. A.
Shkalikov
, “Sturm–Liouville operators with singular potentials
,” Mat. Zametki
66
(6
), 897
–912
(1999
) (in Russian)A. M.
Savchuk
and A. A.
Shkalikov
, [Math. Notes
66
(5-6
), 741
–753
(1999
) (in English)].28.
A. M.
Savchuk
and A. A.
Shkalikov
, “Sturm–Liouville operators with distribution potentials
,” Tr. Mosk. Mat. Obs.
64
, 159
–212
(2003
) (in Russian)A. M.
Savchuk
and A. A.
Shkalikov
, [Trans. Moscow Math. Soc.
64
, 143
–192
(2003
) (in English)]; e-print arXiv:math/0301077.29.
A. M.
Savchuk
and A. A.
Shkalikov
, “Inverse problem for Sturm–Liouville operators with distribution potentials: Reconstruction from two spectra
,” Russ. J. Math. Phys.
12
(4
), 507
–514
(2005
).30.
A. A.
Shkalikov
and Zh.
Ben Amara
, “Oscillation theorems for Sturm–Liouville problems with distribution potentials
,” Vestnik Moskov. Univ. Ser. I: Mat. Mekh.
69
(3
), 43
–49
(2009
) (in Russian)A. A.
Shkalikov
and Zh.
Ben Amara
, [Moscow Univ. Math. Bull.
64
(3
), 132
–137
(2009
) (in English)].© 2019 Author(s).
2019
Author(s)
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