Semiclassical Trace Formula and Spectral Shift Function for Systems via a Stationary Approach

被引:3
|
作者
Assal, Marouane [1 ]
Dimassi, Mouez [1 ]
Fujiie, Setsuro [2 ]
机构
[1] Univ Bordeaux, CNRS, UMR 5251, IMB, 351 Cours Liberat, F-33405 Talence, France
[2] Ritsumeikan Univ, 1-1-1 Noji Higashi, Kusatsu 5258577, Japan
关键词
SCATTERING SOLUTIONS; ASYMPTOTIC-BEHAVIOR; HIGH-ENERGY; TIME-DECAY; RESOLVENT; OPERATORS; PHASE; PERTURBATIONS; RESONANCES; BOUNDS;
D O I
10.1093/imrn/rnx149
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the spectral shift function for a pair of selfadjoint Schrodinger operators with matrix-valued potentials. We give Weyl-type semiclassical asymptotics with sharp remainder estimate for the spectral shift function, and, under the existence condition of a scalar escape function, a full asymptotic expansion in the strong sense for its derivative. These results are consequences of semiclassical trace formulas for general microhyperbolic systems, possibly with eigenvalue crossings, obtained by a time-independent approach.
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页码:1227 / 1264
页数:38
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