Inverse Scattering on the Half-Line Revisited
نویسندگان
چکیده
منابع مشابه
Inverse Resonance Scattering on the Half Line
For the Schrr odinger operator on the half line we prove the following results: the mapping from real compactly supported potentials to the associated Jost functions (in some class of entire functions) is one-to-one and onto. Moreover, we prove that such potential is uniquely determined by its bound states and resonances.
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Recently A. G. Ramm (1999) has shown that a subset of phase shifts δl, l = 0, 1, . . ., determines the potential if the indices of the known shifts satisfy the Müntz condition ∑ l =0,l∈L 1 l = ∞. We prove the necessity of this condition in some classes of potentials. The problem is reduced to an inverse eigenvalue problem for the half-line Schrödinger operators.
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ژورنال
عنوان ژورنال: Reports on Mathematical Physics
سال: 2015
ISSN: 0034-4877
DOI: 10.1016/s0034-4877(15)30026-4