Inverse problems for differential operators with nonseparated boundary conditions in the central symmetric case
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V. A. Marchenko, Sturm-Liouville operators and their applications, Naukova Dumka, Kiev, 1977; English transl., Birkhauser, 1986.
B. M. Levitan, Inverse Sturm-Liouville problems. Nauka, Moscow, 1984; English transl., VNU Sci. Press, Utrecht, 1987.
J. Poschel and E. Trubowitz, Inverse Spectral Theory, Academic Press, New York, 1987.
G. Freiling and V. A. Yurko, Inverse Sturm-Liouville Problems and their Applications. NOVA Science Publishers, New York, 2001.
V. A. Yurko, Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-posed Problems Series. VSP, Utrecht, 2002.
I. V. Stankevich, An inverse problem of spectral analysis for Hill's equation, Doklady Akad. Nauk SSSR, 192, no.1(1970), 34--37. (in Russian); English transl. in Soviet Math. Dokl., 11(1970), 582--586.
V. A. Marchenko and I. V. Ostrovskii, A characterization of the spectrum of the Hill operator, Mathem. Sb., 97(1975), 540--606 (in Russian); English transl. in Math. USSR-Sb., 26(1975), 493--554.
V. A. Yurko, An inverse problem for second order differential operators with regular boundary conditions, Matem. Zametki, 18, no.4 (1975), 569--576 (in Russian); English transl. in Mathematical Notes, 18(1975), 928--932.
V. A. Yurko, On a periodic boundary value problem, Differ. Equations and Theory of Functions, Saratov Uni., Saratov, 1981, 109-115 (in Russian).
V. A. Yurko, On recovering differential operators with nonseparated boundary conditions, Study in Math. and Appl., Bashkir Uni., Ufa, 1981, 55-58 (in Russian).
O. A. Plaksina, Inverse problems of spectral analysis for the Sturm-Liouville operators with nonseparated boundary conditions, Mathem. Sb., 131(1986), 3--26 (in Russian); English transl. in Math. USSR-Sb.59(1988), 1--23.
I. M. Guseinov, M. G. Gasymov and I. M. Nabiev, An inverse problem for the Sturm-Liouville operator with nonseparable self-adjoint boundary conditions, Sib. Mathem. Zh., 31(1990), 46--54 (in Russian); English
trans. in Siberian Math. J., 31(1990), 910--918.
I. M. Guseinov and I. M. Nabiev, Solution of a class of inverse boundary-value Sturm-Liouville problems, Mathem. Sb., 186(1995),35--48 (in Russian); English transl. in Sbornik: Mathematics, 186(1995), 661--674.
P. Kargaev and E. Korotyaev, The inverse problem for the Hill operator, a direct approach, Invent. Math., 129(1997), 567-593.
V. A. Yurko, On differential operators with nonseparated boundary conditions, Funkt. Analiz i Prilozh., 28 (1994), 90--92 (Russian); English transl. in Functional Analysis and Applications, 28(1994), 295--297.
V. A. Yurko, The inverse spectral problem for differential operators with nonseparated boundary conditions, Journal of Mathematical Analysis and Applications, 250(2000), 266--289.
G. Freiling and V. A. Yurko, On the stability of constructing a potential in the central symmetry case, Applicable Analysis, 90(2011), 1819--1828.
Y. P. Wang, Inverse problems for discontinuos Sturm-Liouville operators with mixed spectral data, Inverse Problems in Sci. Eng.,23(2015), 1180--1198.
Y. P. Wang, C. F. Yang and Z. Y. Huang, Reconstruction for the spherically symmetric speed of sound from nodal data, Inverse Problems in Sci. Eng., 21(2013), 1032--1046.
C. T. Shieh and V. A. Yurko, Inverse spectral and nodal problems for discontinuous boundary value problems, Journal of Mathematical Analysis and Applications, 347(2008), 266--272.