Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

Request Permissions   Purchase Content 


Riemann-Hilbert approach to the inverse problem for the Schrödinger operator on the half-line

Authors: R. Shterenberg and V. Sukhanov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 6.
Journal: St. Petersburg Math. J. 26 (2015), 1005-1017
MSC (2010): Primary 34A55, 34L40
Published electronically: September 21, 2015
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A simple yet complete construction of the inverse problem for the
Schrödinger operator on the half-line is presented in terms of the Riemann-Hilbert approach.

References [Enhancements On Off] (What's this?)

  • 1. L. D. Faddeev, Inverse problem of the quantum scattering theory, Uspekhi Mat. Nauk 14 (1959), no. 4, 57-119. (Russian) MR 0110466 (22:1344)
  • 2. V. A. Marchenko, Sturm-Liouville operators and their applications, Naukova Dumka, Kiev, 1977; English transl., Birkhauser, Basel, 1986. MR 0897106 (88f:34034)
  • 3. Z. S. Agranovich and V. A. Marchenko, The inverse problem of scattering theory, Khar'kov. Univ., Khar'kov, 1960; English transl., Gordon and Breach Sci. Publ., New York-London, 1963. MR 0162497 (28:5696)
  • 4. R. G. Shterenberg and V. V. Sukhanov, Scattering for differential operators of order four on the half-line, I, Direct problem, Algebra i Analiz 25 (2013), no. 2, 236-251; English transl., St. Petersburg. Math. J. 25 (2014), no. 2, 327-337. MR 3114857
  • 5. R. Beals, P. Deift, and C. Tomei, Direct and inverse scattering on the line, Math. Surveys Monogr., vol. 28, Amer. Math. Soc., Providence, RI, 1988. MR 954382 (90a:58064)
  • 6. P. Deift and X. Zhou, Direct and inverse scattering on the line with arbitrary singularities, Comm. Pure Appl. Math. 44 (1991), no. 5, 485-533. MR 1105873 (92g:34112)
  • 7. B. A. Levitan and I. S. Sargsyan, Introduction to spectral theory: self-adjoint ordinary differential operators, Nauka, Moscow, 1970; English transl., Math. Monogr., vol. 39, Amer. Math. Soc., Providence, RI, 1975. MR 0369797 (51:6026)
  • 8. F. D. Gakhov, Boundary value problems, Fizmatgiz, Moscow, 1963; English transl., Pergamon Press, Oxford-New York, 1966. MR 0198152 (33:6311)
  • 9. N. P. Vekua, Systems of singular integral equations, Nauka, Moscow 1970; English transl., P. Noordhoff, Ltd., Groningen, 1967. MR 0211220 (35:2102)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 34A55, 34L40

Retrieve articles in all journals with MSC (2010): 34A55, 34L40

Additional Information

R. Shterenberg
Affiliation: Department of Mathematics, University of Alabama at Birmingham, 1300 University Boulevard, Birmingham, Alabama 35294-1170

V. Sukhanov
Affiliation: Department of Mathematical Physics, Institute of Physics, St. Petersburg State University, Ulyanovskaya Str. 1, Petrodworetz, 198904, St. Petersburg, Russia

Keywords: Schr\"odinger operator, inverse problem, Riemann--Hilbert problem
Received by editor(s): August 12, 2013
Published electronically: September 21, 2015
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society