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2013 | 11 | 12 | 2203-2214
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An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point

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EN
We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.
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Bibliografia
  • [1] Chadan K., Colton D., Päivärinta L., Rundell W., An Introduction to Inverse Scattering and Inverse Spectral Problems, SIAM Monogr. Math. Model. Comput., SIAM, Philadelphia, 1997 http://dx.doi.org/10.1137/1.9780898719710
  • [2] Constantin A., On the inverse spectral problem for the Camassa-Holm equation, J. Funct. Anal., 1998, 155(2), 352–363 http://dx.doi.org/10.1006/jfan.1997.3231
  • [3] Fedoseev A., Inverse problems for differential equations on the half-line having a singularity in an interior point, Tamkang J. Math., 2011, 42(3), 343–354 http://dx.doi.org/10.5556/j.tkjm.42.2011.343-354
  • [4] Fedoseev A.E., Inverse problem for Sturm-Liouville operator on the half-line having nonintegrable singularity in an interior point, Izvestiya Saratovskogo Universiteta, Mat. Mekh. Inform., 2012, 12(4), 49–55 (in Russian)
  • [5] Freiling G., Yurko V., Reconstructing parameters of a medium from incomplete spectral information, Results Math., 1999, 35(3–4), 228–249 http://dx.doi.org/10.1007/BF03322815
  • [6] Freiling G., Yurko V., Inverse Sturm-Liouville Problems and their Applications, NOVA Science, Huntington, 2001
  • [7] Hald O.H., Discontinuous inverse eigenvalue problems, Comm. Pure Appl. Math., 1984, 37(5), 539–577 http://dx.doi.org/10.1002/cpa.3160370502
  • [8] Lapwood E.R., Usami T., Free Oscillations of the Earth, Cambridge Monogr. Mech. Appl. Math., Cambridge University Press, Cambridge, 1981
  • [9] Levitan B.M., Inverse Sturm-Liouville Problems, VVSP, Zeist, 1987
  • [10] Marchenko V.A., Sturm-Liouville Operators and Applications, Oper. Theory Adv. Appl., 22, Birkhäuser, Basel, 1986 http://dx.doi.org/10.1007/978-3-0348-5485-6
  • [11] McLaughlin J.R., Analytical methods for recovering coefficients in differential equations from spectral data, SIAM Rev., 1986, 28(1), 53–72 http://dx.doi.org/10.1137/1028003
  • [12] Shepel’sky D.G., The inverse problem of reconstruction of the medium’s conductivity in a class of discontinuous and increasing functions, In: Spectral Operator Theory and Related Topics, Adv. Soviet Math., 19, American Mathematical Society, Providence, 1994, 209–232
  • [13] Stashevskaya V.V., On inverse problems of spectral analysis for a certain class of differential equations, Dokl. Akad. Nauk SSSR, 1953, 93(3), 409–412 (in Russian)
  • [14] Yurko V.A., An inverse problem for differential equations with a singularity, Differ. Equ., 1992, 28(8), 1100–1107
  • [15] Yurko V.A., On higher-order differential operators with a singular point, Inverse Problems, 1993, 9(4), 495–502 http://dx.doi.org/10.1088/0266-5611/9/4/004
  • [16] Yurko V.A., On higher-order differential operators with a regular singularity, Sb. Math., 1995, 186(6), 901–928 http://dx.doi.org/10.1070/SM1995v186n06ABEH000048
  • [17] Yurko V., Integral transforms connected with discontinuous boundary value problems, Integral Transforms Spec. Funct., 2000, 10(2), 141–164 http://dx.doi.org/10.1080/10652460008819282
  • [18] Yurko V., Method of Spectral Mappings in the Inverse Problem Theory, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2002 http://dx.doi.org/10.1515/9783110940961
  • [19] Yurko V.A., On the reconstruction of singular nonselfadjoint differential operators with a singularity inside an interval, Differ. Equ., 2002, 38(5), 678–694 http://dx.doi.org/10.1023/A:1020214825432
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0315-8
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