Zero energy scattering for one-dimensional Schrödinger operators and applications to dispersive estimates
نویسندگان
چکیده
منابع مشابه
Zero Energy Scattering for One-dimensional Schrödinger Operators and Applications to Dispersive Estimates
We show that for a one-dimensional Schrödinger operator with a potential, whose (j + 1)-th moment is integrable, the j-th derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to improve the known dispersive estimates with integrable time decay for the one-dimensional Schrödinger equation in the resonant case.
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A “resonance” here is defined to take place iff W (0) = 0 where W (λ) is the Wronskian of the two Jost solutions at energy λ2, see the following section. It is known that the spectrum of H is purely absolutely continuous on (0,∞) under our assumptions (V ∈ L1(R) suffices for that) so that Pac is the same as the projection onto the orthogonal complement of the bound states. For the case of three...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society, Series B
سال: 2015
ISSN: 2330-1511
DOI: 10.1090/bproc/19