Scattering problem for the ordinary differential operator of order four on the half-line. I. Direct problem
HTML articles powered by AMS MathViewer
- by
R. Shterenberg and V. Sukhanov
Translated by: the author - St. Petersburg Math. J. 25 (2014), 327-337
- DOI: https://doi.org/10.1090/S1061-0022-2014-01293-9
- Published electronically: March 12, 2014
- PDF | Request permission
Abstract:
Direct and inverse spectral problems are studies for ordinary differential operators of order four on the half-line. This first part of the text is devoted to the study of the direct problem.References
- Richard Beals, Percy Deift, and Carlos Tomei, Direct and inverse scattering on the line, Mathematical Surveys and Monographs, vol. 28, American Mathematical Society, Providence, RI, 1988. MR 954382, DOI 10.1090/surv/028
- P. Deift and E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979), no. 2, 121–251. MR 512420, DOI 10.1002/cpa.3160320202
- Percy Deift and Xin Zhou, Direct and inverse scattering on the line with arbitrary singularities, Comm. Pure Appl. Math. 44 (1991), no. 5, 485–533. MR 1105873, DOI 10.1002/cpa.3160440502
- V. V. Sukhanov, An inverse problem for a selfadjoint differential operator on the axis, Mat. Sb. (N.S.) 137(179) (1988), no. 2, 242–259, 271–272 (Russian); English transl., Math. USSR-Sb. 65 (1990), no. 1, 249–266. MR 971696, DOI 10.1070/SM1990v065n01ABEH001144
- J. Östensson, Trace formulae and spectral properties of fourth order differential operators, KTH, PhD-thesis.
- A. Laptev, R. Shterenberg, V. Sukhanov, and J. Östensson, Reflectionless potentials for an ordinary differential operator of order four, Inverse Problems 22 (2006), no. 1, 135–153. MR 2194188, DOI 10.1088/0266-5611/22/1/008
Bibliographic Information
- R. Shterenberg
- Affiliation: Department of Mathematics, University of Alabama at Birmingham, 1300 University Blvd, Birmingham, Alabama 35294
- Email: rshterenberg@gmail.com
- V. Sukhanov
- Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 3, Petrodvorets, St. Petersburg 185504, Russia
- Email: vvsukhanov@mail.ru
- Received by editor(s): November 5, 2012
- Published electronically: March 12, 2014
- Additional Notes: Supported by RFBR (grant no. 05-01-01076)
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 327-337
- MSC (2010): Primary 34L25
- DOI: https://doi.org/10.1090/S1061-0022-2014-01293-9
- MathSciNet review: 3114857
Dedicated: Dedicated to the memory of V. S. Buslaev