Sturm-Liouville operators are considered on a finite interval with the so-called transmission (discontinuous, jump) conditions in interior points. The inverse problem of recovering operators from their spectral characteristics is studied. Uniqueness theorems are provided for this class of inverse problems. The authors use the method and techniques from the monograph [G. Freiling
and V. A. Yurko
, Inverse Sturm-Liouville Problems and their Applications. Huntington, NY: Nova Science Publishers. (2001; Zbl 1037.34005
)]; and from the papers [V. A. Yurko
, “Integral transforms connected with discontinuous boundary value problems”, Integral Transforms Spec. Funct. 10, No. 2, 141–164 (2000; Zbl 0989.34015
), “On boundary value problems with jump conditions inside the interval”, Differ. Equ. 36, No. 8, 1266–1269 (2000); translation from Differ. Uravn. 36, No. 8, 1139–1140 (2000; Zbl 0991.34028
)], where this class of inverse problems was previously well studied. In these three works besides proven uniqueness theorems, also procedures for constructing solutions were provided, and the characterization of the spectral data was obtained.