Akcay, Ozge

This paper deals with the investigation of the direct scattering problem for the Sturm-Liouville operator containing both the discontinuous coefficient and discontinuity conditions at some point on the positive half-line. The integral representation of the Jost solution is obtained and the properties of its kernel function are given. A total collection of the scattering data is constructed and the behavior of the scattering function at infinity is examined.

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