Voir la notice de l'article provenant de la source Math-Net.Ru
@article{EMJ_2012_3_4_a1, author = {A. M. Akhtyamov and V. A. Sadovnichy and Ya. T. Sultanaev}, title = {Generalizations of {Borg's} uniqueness theorem to the case of nonseparated boundary conditions}, journal = {Eurasian mathematical journal}, pages = {10--22}, publisher = {mathdoc}, volume = {3}, number = {4}, year = {2012}, language = {en}, url = {http://geodesic.mathdoc.fr/item/EMJ_2012_3_4_a1/} }
TY - JOUR AU - A. M. Akhtyamov AU - V. A. Sadovnichy AU - Ya. T. Sultanaev TI - Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions JO - Eurasian mathematical journal PY - 2012 SP - 10 EP - 22 VL - 3 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/EMJ_2012_3_4_a1/ LA - en ID - EMJ_2012_3_4_a1 ER -
%0 Journal Article %A A. M. Akhtyamov %A V. A. Sadovnichy %A Ya. T. Sultanaev %T Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions %J Eurasian mathematical journal %D 2012 %P 10-22 %V 3 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/EMJ_2012_3_4_a1/ %G en %F EMJ_2012_3_4_a1
A. M. Akhtyamov; V. A. Sadovnichy; Ya. T. Sultanaev. Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions. Eurasian mathematical journal, Tome 3 (2012) no. 4, pp. 10-22. http://geodesic.mathdoc.fr/item/EMJ_2012_3_4_a1/
[1] A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Inverse Problem for an Operator Pencil with Nonseparated Boundary Conditions”, Eurasian Mathematical Journal, 1:2 (2010), 5–16 | MR | Zbl
[2] V. A. Ambarzumijan, “Uber eine Frage der Eigenwerttheorie”, Zeitshrift fur Physik, 53 (1929), 690–695 | DOI
[3] A. L. Andrew, “Computing Sturm–Liouville Potentials from two Spectra”, Inverse Problems, 22 (2006), 2069–2081 | DOI | MR | Zbl
[4] P. A. Binding, H. Volkmer, “Inverse Oscillation Theory for Sturm–Liouville Problems with Nonseparated Boundary Conditions”, Inverse Probl., 23:1 (2007), 343–356 | DOI | MR
[5] P. A. Binding, B. A. Watson, “An Inverse Nodal Problem for Two–Parameter Sturm–Liouville Systems”, Inverse Problems, 25 (2009), 1–19 | DOI | MR
[6] G. Borg, “Eine Umkehrung der Sturm Liouvilleschen Eigenwertanfgabe. Bestimmung der Differentialgleichung durch die Eigenwarte”, Acta Math., 78:1 (1946), 1–96 | DOI | MR | Zbl
[7] L. A. Chudov, “The Inverse Sturm–Liouville Problem”, Mat. Sb. (N.S.), 25(67):3 (1949), 451–456 (in Russian) | MR | Zbl
[8] Siberian Math. J., 31:6 (1990), 910–918 | DOI | MR | Zbl
[9] N. J. Guliyev, “Inverse Eigenvalue Problems for Sturm–Liouville Equations with Spectral Parameter Linearly Contained in One of The Boundary Conditions”, Inverse Problems, 21 (2005), 1315–1330 | DOI | MR | Zbl
[10] Math. Sb., 186:5 (1995), 661–674 | DOI | MR | Zbl
[11] Math. Sb., 198:11 (2007), 1579–1598 | DOI | DOI | MR | Zbl
[12] A. Kammanee, C. Böckmann, “Boundary Value Method for Inverse Sturm–Liouville Problems”, Applied Mathematics and computation, 214 (2009), 342–352 | DOI | MR | Zbl
[13] B. E. Kanguzhin, Uniqueness Theorems for Spectral Analysis of Inverse Problems with Nonseparated Boundary Conditions, Dep. in VINITI, 1982, 73 pp. (in Russian)
[14] T. M. Karaseva, “On The Inverse Sturm–Liouville Problem for a Non-Hermitian Operator”, Mat. Sb. (N.S.), 32(74):2 (1953), 477–484 (in Russian) | MR | Zbl
[15] A. Kostenko, A. Sakhnovich, G. Tesch, “Inverse Eigenvalue Problems for Perturbed Spherical Schrödinger Operators”, Inverse Problems, 26:10 (2010), 1–14 | DOI | MR
[16] M. G. Krein, “Solution of the Inverse Sturm–Liouville Problem”, Dokl. Akad. Nauk SSSR, 76:1 (1951), 21–24 (in Russian) | MR
[17] M. G. Krein, “Determination of the Density of a Non-Homogeneous Symmetric Cord by Its Frequency Spectrum”, Dokl. Akad. Nauk SSSR (N.S.), 76:3 (1951), 345–348 (in Russian) | MR
[18] N. Levinson, “The Inverse Sturm–Liouville Problem”, Math. Tidsskr. Ser. B, 13 (1949), 25–30 | MR
[19] VNU Science Press, Utrecht, 1987 | MR | Zbl | Zbl
[20] B. M. Levitan, I. S. Sargsjan, Sturm–Liouville and Dirac Operators, Nauka, Moscow, 1988 | MR | Zbl
[21] Russian Mathematical Surveys, 19:2 (1964), 1–63 | DOI | MR | Zbl
[22] V. A. Marchenko, “Certain Problems In The Theory Of Second-Order Differential Operators”, Doklady Akad. Nauk SSSR, 72:3 (1950), 457–460 (in Russian) | MR | Zbl
[23] V. A. Marchenko, Spectral Theory of Sturm–Liouville Operators, Naukova Dumka, Kiev, 1972 (in Russian) | MR | Zbl
[24] Math. USSR Sb., 26:4 (1975), 493–554 | DOI | MR | Zbl
[25] Birkhäuser, Basel, 1986 | MR | Zbl
[26] Parts I, II, Ungar, New York, 1967, 1968 | MR | Zbl | Zbl
[27] L. Nizhnik, “Inverse Nonlocal Sturm–Liouville Problem”, Inverse Problems, 26 (2010), 1–9 | DOI | MR
[28] Math. USSR Sb., 59:1 (1988), 1–23 | DOI | MR | Zbl | Zbl
[29] O. A. Plaksina, “Inverse Problems of Spectral Analysis for Sturm–Liouville Operators with Nonseparated Boundary Conditions. II”, Math. Ussr. Sb., 136(178):1 (1989), 140–159 (in Russian) | MR | Zbl
[30] V. A. Sadovnichy, “Uniqueness of the Solution of The Inverse Problem for Second-Order Differential Equation with Nonseparated Boundary Conditions, Regularized Sums of Eigenvalues. Factorization of the Characteristic Determinant”, Dokl. Akad. Nauk SSSR, 206:2 (1972), 293–296 | MR
[31] V. A. Sadovnichy, B. E. Kanguzhin, “On a Connection Between the Spectrum of A Differential Operator with Symmetric Coefficients and Boundary Conditions”, Dokl. Akad. Nauk SSSR, 267:2 (1982), 310–313 (in Russian) | MR
[32] Doklady Mathematics, 60:1 (1999), 115–117 | MR
[33] Doklady Mathematical Sciences, 69:2 (2004), 105–107 | MR
[34] Doklady Mathematics, 74:3 (2006), 889–892 | DOI | MR
[35] Doklady Mathematics, 75:1 (2007), 20–22 | DOI | MR
[36] Doklady Mathematics, 79:2 (2009), 169–171 | DOI | MR
[37] V. A. Sadovnichy, Ya. T. Sultanaev, A. M. Akhtyamov, Inverse Sturm–Liouville Problems with Nonseparated Boundary Conditions, MSU, Moscow, 2009 (in Russian)
[38] Doklady Mathematics, 83:3 (2011), 302–305 | DOI | MR | MR
[39] L. A. Sakhnovich, “Inverse Problem for Differential Operators of Order $n>2$ with Analytic Coefficients”, Mat. Sb. (N.S.), 46(88):1 (1958), 61–76 (in Russian) | MR | Zbl
[40] Functional Analysis and Its Applications, 44:4 (2010), 270–285 | DOI | DOI | MR | Zbl
[41] Sov. Math. Dokl., 11 (1970), 582–586 | MR
[42] A. N. Tikhonov, “On Uniqueness of Solution of the Electroprospecting Problem”, Dokl. Akad. Nauk SSSR, 69:6 (1949), 797–800 (in Russian) | MR | Zbl
[43] Math. Notes, 18:3–4 (1975), 928–932 | DOI | MR | Zbl
[44] V. A. Yurko, “The Inverse Spectral Problems for Differential Operators with Nonseparated Boundary Conditions”, Journal of Mathematical Analysis and Applications, 250 (2000), 266–289 | DOI | MR | Zbl
[45] V. A. Yurko, Inverse Spectral Problems for Differential Operators and their Applications, Gordon and Breach, Amsterdam, 2000 | MR | Zbl