Recovering Differential Operators on the Half-Line with Indefinite Discontinuous Weights

Authors

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3721

Keywords:

differential operators; indefinite discontinuous weights; inverse spectral problems; method of spectral mappings.

Abstract

Non-self-adjoint second-order differential operators on the half-line with indefinite discontinuous weights are studied. Properties of spectral characteristics are established and inverse problems of recovering operators from their spectral characteristics are investigated. For these class of nonlinear inverse problems algorithms for constructing the global solutions are developed, and uniqueness theorems are proved

Author Biography

Vyacheslav Anatol'evich Yurko, Saratov State University

Professor

Department of Mathematics

References

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McHugh J. An historical survey of ordinary linear differential equations with a large parameter and turning points, Arch. Hist. Exact. Sci. 7 (1970), 277-324.

Daho K. and Langer H. Sturm-Liouville operators with an indefinite weight functions, Proc. Roy. Soc. Edinburgh Sect. A 78 (1977), 161-191.

Freiling G. and Yurko V. Inverse Sturm-Liouville Problems and Their Applications, NOVA Science Publishers, New York, 2001.

Freiling G. and Yurko V.A. Inverse spectral problems for differential equations on the half-line with turning points. Journal of Differential Equations, 154, no.2 (1999), 419-453.

Yurko V.A. Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series, VSP, Utrecht, 2002.

Freiling G. and Yurko V.A. Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point. nverse Problems, 18, no.3 (2002), 757-773.

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Published

2021-01-31

How to Cite

Yurko, . V. A. (2021). Recovering Differential Operators on the Half-Line with Indefinite Discontinuous Weights. Tamkang Journal of Mathematics, 52(1), 155-169. https://doi.org/10.5556/j.tkjm.52.2021.3721