Hill’s equation, modified by a potential that vanishes as x → ±∞, is considered. The direct scattering problem is studied; analytic and asymptotic properties of solutions of Hill’s equation as well as of solutions of the modified equation are established. A new version of Levinson’s theorem is proved. The inverse scattering problem is solved by means of a Marchenko-like equation.
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Roger G. Newton (1983) studied this question.
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