论文标题
Bochner-Schrödinger操作员功能的半经典渐近扩展
Semiclassical asymptotic expansions for functions of the Bochner-Schrödinger operator
论文作者
论文摘要
Bochner-Schrödinger操作员$ h_ {p} = \ frac1pΔ^{l^p \ otimes e}+v $ tensor powers $ l^p $ l^p $ twellmantian vector bundle $ e $ twested twessed bunde $ l $ l $ l $ l $ l $ l $ l $ l $ e $ e $ e $ e $在riemannian ficounded bectection byemann filolded bectection in Bounded Geemented Ins tocemented Ins Insed Ins tocemented Ins tocemented。对于任何功能$φ\ in \ Mathcal s（\ MathBb r）$，我们考虑了$ l^2（x，x，l^p \ otime e）$ in Spectral Therorem定义的有限的线性运算符$φ（H_P）$（H_P）$，并描述了其在固定的nefly of diemclascal $ plascal $ plascal $ plascal $ $ plascal $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $的线性的线性操作员$φ\ in中。特别是，我们证明了操作员$φ（H_P）$的痕迹允许$ p^{ - 1/2} $的完整渐近扩展为$ p \ to \ to \ infty $。
The Bochner-Schrödinger operator $H_{p}=\frac 1pΔ^{L^p\otimes E}+V$ on tensor powers $L^p$ of a Hermitian line bundle $L$ twisted by a Hermitian vector bundle $E$ on a Riemannian manifold of bounded geometry is studied. For any function $φ\in \mathcal S(\mathbb R)$, we consider the bounded linear operator $φ(H_p)$ in $L^2(X,L^p\otimes E)$ defined by the spectral theorem and describe an asymptotic expansion of its smooth Schwartz kernel in a fixed neighborhood of the diagonal in the semiclassical limit $p\to \infty$. In particular, we prove that the trace of the operator $φ(H_p)$ admits a complete asymptotic expansion in powers of $p^{-1/2}$ as $p\to \infty$.
