Abstract
We study representations of solutions of the Dirac equation, properties of spectral data, and inverse problems for the Dirac operator on a finite interval with discontinuity conditions inside the interval.
Similar content being viewed by others
REFERENCES
B. M. Levitan, and I. S. Sargsyan, Sturm-Liouville and Dirac Operators [in Russian], Nauka, Moscow (1988).
V. A. Marchenko, Sturm-Liouville Operators and Their Applications [in Russian], Naukova Dumka, Kiev (1977).
Yu. M. Berezanskii, “Uniqueness theorem in the inverse spectral problem for the Schrodinger equation,” Tr. Mosk. Mat. Obshch., 7, 3–51 (1958).
L. P. Nizhnik, Inverse Scattering Problems for Hyperbolic Equations [in Russian], Naukova Dumka, Kiev (1977).
M. G. Gasymov, “Inverse problem of the scattering theory for Dirac systems of order 2n,” Tr. Mosk. Mat. Obshch., 19, 41–112 (1968).
M. G. Gasymov, and T. T. Dzhabiev, “Determination of a system of Dirac differential equations using two spectra,” in: Proceedings of School-Seminar on the Spectral Theory of Operators and Representations of Group Theory [in Russian], Elm, Baku (1975), pp. 46–71.
I. M. Guseinov, “On the representation of Jost solutions of a system of Dirac differential equations with discontinuous coefficients,” Izv. Akad. Nauk Azerb. SSR, No. 5, 41–45 (1999).
O. H. Hald, “Discontinuous inverse eigenvalue problems,” Comm. Pure Appl. Math., 37, 539–577 (1984).
D. Shepelsky, “The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions,” Spectral Oper. Theory Rel. Topics: Adv. Sov. Math., 19, 209–232 (1994).
M. Kobayashi, “A uniqueness proof for discontinuous inverse Sturm-Liouville problems with symmetric potentials,” Inverse Probl., 5, No.5, 767–781 (1989).
R. Kh. Amirov, and V. A. Yurko, “On differential operators with singularity and discontinuity conditions inside an interval,” Ukr. Mat. Zh., 53, No.11, 1443–1457 (2001).
V. A. Yurko, “Integral transforms connected with discontinuous boundary-value problems,” Int. Trans. Spec. Funct., 10, No.2, 141–164 (2000).
B. Ya. Levin, Entire Functions [in Russian], Moscow University, Moscow (1971).
V. F. Zhdanovich, “Formulas for the zeros of Dirichlet polynomials and quasipolynomials,” Dokl. Akad. Nauk SSSR, 135, No.8, 1046–1049 (1960).
M. G. Krein, and B. Ya. Levin, “On entire almost periodic functions of exponential type,” Dokl. Akad. Nauk SSSR, 64, No.3, 285–287 (1948).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 601–613, May, 2005.
Rights and permissions
About this article
Cite this article
Amirov, R.K. On a System of Dirac Differential Equations with Discontinuity Conditions Inside an Interval. Ukr Math J 57, 712–727 (2005). https://doi.org/10.1007/s11253-005-0222-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-005-0222-7