Low energy resolvent estimates and continuity of time-delay operators
1987 ◽
Vol 105
(1)
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pp. 229-242
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SynopsisIn this paper, we are interested in the L2-continuity of the Eisenbud–Wigner time-delay operator in potential scattering theory. Using the ideas due to Jensen–Kato [5], we first establish some low energy estimates on the resolvent of the Schrödinger operator and its derivative in weighted Sobolev spaces. Then applying these results together with the global decay of the wave functions (Lemma 3.2), we show that the Eisenbud–Wigner time-delay operator extends to a bounded operator on L2(Rn) with n ≧ 4, on condition that the potential V(x) decreases as fast as 0(|x | −4−ε) at infinity and that 0 is neither the eigenvalue nor the resonance for the Schrodinger operator –Δ + V for n = 4 or 5.
2020 ◽
Vol 278
(4)
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pp. 108350
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1984 ◽
Vol 124
(1-3)
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pp. 413-417
2008 ◽
Vol 33
(1)
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pp. 19-44
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Keyword(s):
1994 ◽
Vol 181
(3)
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pp. 600-625
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Keyword(s):
1994 ◽
Vol 114
(1)
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pp. 168-198
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Keyword(s):