发表刊物：Submitted

摘要：Let \(\Omega \Subset \mathbb{D}\) be a finitely connected domain with $C^3$ boundary and \(T_{\Omega}^{(\alpha)}\) be the weighted Bergman Toeplitz operator with symbol \(\chi_{\Omega}\). For admissible continuous functions $f$ on $[0,1]$, we prove that \[ \operatorname{tr}f(T_\Omega^{(\alpha)}) =\frac{s(\partial\Omega)}{2\pi}M(f)\sqrt\alpha+o(\sqrt\alpha), \] where $M(f)$ is a one-dimensional functional determined by the complementary error-function, and $s(\partial\Omega)$ is the hyperbolic length of $\partial \Omega$. This yields a two-term Szeg\H{o}-type asymptotic formula for Bergman Toeplitz operators, with a leading term determined by the hyperbolic area and a second-order term determined by the hyperbolic length of the boundary. As applications of our results, we derive hyperbolic area laws for the von Neumann and R\'enyi entropies, together with corresponding trace asymptotic formulas for Cauchy wavelet localization operators.

合写作者：Wei Dai, Pan Ma, Fugang Yan, Quan Zhao

是否译文：否