Geodesic
Connection of the different types of inverse data for the one-dimensional Schr\"odinger operator on the half-line
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 134-155

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We consider inverse dynamical, spectral, quantum and acoustical scattering problems for the Schrödinger operator on the half line. The goal of the paper is to establish the connections between different types of inverse data for these problems. The central objects which serve as a source for all formulaes are kernels of so-called connecting operators and Krein equations. 
@article{ZNSL_2016_451_a8,
     author = {A. S. Mikhaylov and V. S. Mikhaylov},
     title = {Connection of the different types of inverse data for the one-dimensional {Schr\"odinger} operator on the half-line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--155},
     publisher = {mathdoc},
     volume = {451},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_451_a8/}
}
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A. S. Mikhaylov; V. S. Mikhaylov. Connection of the different types of inverse data for the one-dimensional Schr\"odinger operator on the half-line. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 134-155. http://geodesic.mathdoc.fr/item/ZNSL_2016_451_a8/