论文标题
革命凸表面上可量子集成本征的浓度
Concentration of quantum integrable eigenfunctions on a convex surface of revolution
论文作者
论文摘要
令$（s^2，g）$为革命的凸表面，$ h \ subset s^2 $独特的旋转旋转大地测量。令$φ^\ ell_m $为$δ_g$和$ \partial_θ$的关节特征函数的正常基础，这是旋转动作的生成器。主要结果是针对标准化经验度量的弱 - *限制的明确公式，$σ_{m = - \ ell}^\ ell ||φ^\ ell_m ||^2_ {l^2（h）}δ__{明确的公式表明，零散的限制特征函数的$ l^2 $规范对于区域特征功能$ m = 0 $，高斯梁的最大值，高斯梁$ m = \ pm 1 $，并展示a $（1- c^2）^{ - c^2）^{ - \ freac at at aintione AT对于伪分化操作员$ b $，我们还计算了归一化度量的限制，$ \ sum_ {m = - \ ell}^\ ell \ langle b或b或e el_m，φ^\ ell_m \ ell_m \ ell_m \ rangleuangletueΔ_
Let $(S^2,g)$ be a convex surface of revolution and $H \subset S^2$ the unique rotationally invariant geodesic. Let $φ^\ell_m$ be the orthonormal basis of joint eigenfunctions of $Δ_g$ and $\partial_θ$, the generator of the rotation action. The main result is an explicit formula for the weak-* limit of the normalized empirical measures, $Σ_{m = -\ell}^\ell ||φ^\ell_m||^2_{L^2(H)} δ_{\frac{m}{\ell}}(c)$ on $[-1,1]$. The explicit formula shows that, asymptotically, the $L^2$ norms of restricted eigenfunctions are minimal for the zonal eigenfunction $m = 0$, maximal for Gaussian beams $m = \pm 1$, and exhibit a $(1 - c^2)^{-\frac{1}{2}}$ type singularity at the endpoints. For a pseudo-differential operator $B$ we also compute the limits of the normalized measures $\sum_{m = -\ell}^\ell \langle B φ^\ell_m , φ^\ell_m \rangle δ_{\frac{m}{\ell}}(c)$.
