Abstract
The inverse phase-type scattering problem for the boundary-value problem−y″+q(x)y=k 2 y (0⩽x<∞), (1)y′ (0)=hy (0) (2) is studied. It is shown that, for each function δ(k) satisfying the hypotheses of Levinson's theorem, there exists a problem (1)–(2) with h≠∞ and another problem (1)–(2) with h=∞ (i.e., with the boundary condition o (0)=0). The solvability condition for the Riemann-Hilbert problem is used more directly than has been done heretofore by others in deriving boundary condition (2).
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Translated from Matematicheskii Zametki, Vol. 17, No. 4, pp. 611–624, April, 1975.
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Levitan, B.M. The inverse scattering problem of quantum theory. Mathematical Notes of the Academy of Sciences of the USSR 17, 363–371 (1975). https://doi.org/10.1007/BF01105389
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DOI: https://doi.org/10.1007/BF01105389