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

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2019年 / 2019卷 / 04期

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.

引用

页码：1227 / 1264

页数：38

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