References
- Anderssen RS. The effect of discontinuities in density and shear velocity on the asymptotic overtone structure of tortional eigenfrequencies of the earth. Geophys. J. R. Astr. Soc. 1997;50:303–309.
- Vinokurov VA, Sadovnichii VA. The eigenvalue and the trace of the Sturm-Liouville operator as differentiable functions of an integrable potential. Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.]. 1999;365:295–297.
- Krueger RJ, Krueger RJ. Inverse problems for nonabsorbing media with discontinuous material properties. J. Math. Phys. 1982;23:396–404.
- Lapwood FR, Usami T. Free oscillations of the earth. Cambridge: Cambridge Univ. Press; 1981.
- Lax PD. Trace formulas for the Schrödinger operator. Comm. Pure Appl. Math. 1994;47:503–512.
- Levitan BM. Calculation of a regularized trace for the Sturm-Liouville operator. Uspekhi Mat. Nauk [Russian Math. Surveys]. 1964;19:161–165.
- Yurko VA. Integral transforms connected with discontinuous boundary value problems. Integral Transforms Spec. Funct. 2000;10:141–164.
- Dikii LA. On a formula of Gel’fand-Levitan. Uspekhi Math. Nauk (in Russian). 1953;8:119–123.
- Yurko VA. Method of spectral mappings in the inverse problem theory: Inverse Ill-posed Probl.Ser. Utrecht: VSP; 2002.
- Freiling G, Yurko VA. Inverse Sturm-Liouville problems and their applications. New York: NOVA Science Publishers; 2001.
- Gelfand M, Levitan BM. On a simple identity for eigenvalues of the differential operator of second order. Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.]. 1953;88:593–596.
- Lidskii VB, Sadovnichii VA. Regularized sums of the roots of a class of entire functions. Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.]. 1967;176:259–262.
- Makin AS. Trace formulas for the Sturm-Liouville operator with regular boundary conditions. Dokl. Math. 2007;76:702–707.
- McNabb A, Anderssen R, Lapwood E. Asymptotic behaviour of the eigenvalues of a Sturm-Liouville system with discontinuous coefficients. J. Math. Anal. Appl. 1976;54:741–751.
- Papanicolaou VG. Trace formulas and the behaviour of large eigenvalues. SIAM J. Math. Anal. 1995;26:218–237.
- Gesztesy F, Holden H. On trace formulas for Schrödinger-type operators. In: Truhlar DG, Truhlar DG, Simon B (eds.). Multiparticle quantum scattering with applications to nuclear, atomic and molecular physics. New York: Springer; 1997. p. 121–145.
- Sadovnichii VA, Lyubishkin VA. Trace formulas and perturbation theory. Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.]. 1988;300:1064–1066.
- Sadovnichii VA, Podol’skii VE. Traces of differential operators. Differ. Equations. 2009;45:477–493.
- Savchuk AM, Shkalikov AA. Trace formula for Sturm-Liouville operators with singular potentials. Math. Notes. 2001;69:387–400.
- Shepelsky DG. 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. Vol. 19, Amer. Math. Soc. Providence, RI; 1994. p. 209–232.
- Gesztesy F, Holden H, Simon B, Zhao Z. Trace formulae and inverse spectral theory for Schrödinger operators. Bull. Amer. Math. Soc. 1993;29:250–255.
- Halberg CJ, Kramer VA. A generalization of the trace concept. Duke Math. J. 1960;27:607–618.
- Shieh CT, Yurko VA. Inverse nodal and inverse spectral problems for discontinuous boundary value problems. J. Math. Anal. Appl. 2008;347:266–272.
- Hald OH. Discontinuous inverse eigenvalue problems. Comm. Pure Appl. Math. 1984;37:539–577.
- Kaup DJ, Newell AC. An exact solution for a derivative nonlinear Schrödinger equation. J. Math. Phys. 1978;19:798–801.