Abstract
We study semi-classical asymptotics of the Spectral Shift Function (SSF) for long-range trapping perturbations of -h 2 ∆.Without any assumption on the behaviour of the classical trajectories we prove the estimates \({\left\| {R\left( {\lambda + i\tau } \right)} \right\|_{s, - s}} \leqslant C\) exp(Ch -p)for the resolvent R (λ+i τ ). We apply this estimates to obtain a new semi-classical representation formula of the SSF.
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Bruneau, V., Petkov, V. (2001). Semi-Classical Resolvent Estimates and Spectral Asymptotics for Trapping Perturbations. In: Demuth, M., Schulze, BW. (eds) Partial Differential Equations and Spectral Theory. Operator Theory: Advances and Applications, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8231-6_5
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DOI: https://doi.org/10.1007/978-3-0348-8231-6_5
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-8231-6
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