论文标题
$ l^{\ infty} $ husimi eigenfunctions的规范
$L^{\infty} $ norms of Husimi distributions of eigenfunctions
论文作者
论文摘要
Laplace本征函数的Husimi分布是相位空间的特殊类型的特殊类型的特征型征收。它们的弱限制是耶吉曼歧管$（m，g）$上的正顺序基础$ \ {ϕ_j \} $的众所周知的量子限制或微局部缺陷度量。 Husimi分布是特征函数与$ M $的络合力的分析连续性的标准化mod平方，可以用cotangent Bundle $ t^*m $的开放子集确定。 Husimi分布是概率度量，其密度在$ζ$处是相位空间点$ζ$处量子粒子的概率密度。我们对Husimi分布的SUP规范进行了普遍的上限。我们还提供了必要的条件，以通过$ζ$的地理位生类型获得上限。边界很清晰，可以通过复杂的高斯梁来实现。这些结果开辟了一个将Husimi分布的SUP规范（或其他自然规范）与弱 *限制的性质相关的问题。
Husimi distributions of Laplace eigenfunctions are special types of `microlocal lifts' of eigenfunctions to phase space. Their weak * limits are the well-known quantum limits or microlocal defect measures of an orthonormal basis $\{ ϕ_j\}$ of eigenfunctions on a Riemannian manifold $(M,g)$ . Husimi distributions are normalized mod squares of analytic continuations of eigenfunctions to the complexification of $M$, which may be identified with an open subset of the cotangent bundle $T^*M$. Husimi distributions are probability measures whose density at $ζ$ is the probability density of a quantum particle at the phase space point $ζ$. We given universal upper bounds on the sup norms of the Husimi distributions. We also give necessary conditions to obtain the upper bounds in terms of the type of the geodesic through $ζ$. The bounds are sharp and are achieved by complexified Gaussian beams. These results open the question of relating sup norms (or other natural norms) of Husimi distributions to properties of the weak * limits.
