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Low energy resolvent estimates and continuity of time-delay operators

Published online by Cambridge University Press:  14 November 2011

Wang Xue-Ping
Wang Xue-Ping
Affiliation:
U.E.R. de Mathématiques et d'Informatique, Université de Nantes, 44072 Nantes Cédex, France
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Synopsis

In 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 229 - 242
Copyright
Copyright © Royal Society of Edinburgh 1987

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