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On geometrically finite hyperbolic manifolds $\Gamma \setminus {ℍ}^d$, including those with non-maximal rank cusps, we give upper bounds on the number $N\left(R\right)$ of resonances of the Laplacian in disks of size $R$ as $R\to \infty$. In particular, if the parabolic subgroups of $\Gamma$ satisfy a certain Diophantine condition, the bound is $N\left(R\right)=𝒪\left(R^d{\left(\log R\right)}^{d+1}\right)$.

Let $X$ be a compact Kähler manifold with integral Kähler class and $L\to X$ a holomorphic Hermitian line bundle whose curvature is the symplectic form of $X$. Let $H\in C^{\infty }(X,ℝ)$ be a Hamiltonian, and let $T_k$ be the Toeplitz operator with multiplier $H$ acting on the space ${\mathscr{H}}_k=H^0(X,L^{\otimes k})$. We obtain estimates on the eigenvalues and eigensections of $T_k$ as $k\to \infty$, in terms of the classical Hamilton flow of $H$. We study in some detail the case when $X$ is an integral coadjoint orbit of a Lie group.