We give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the K\"ahler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.

中文翻译：

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与平滑 Kähler 势相关的 Bergman 核的定量上限

我们根据 K\"ahler 势的泰勒系数的增长率给出了与平滑正线丛的张量幂相关的 Bergman 核的上限。作为应用，我们获得了改进的非对角线衰减率解析、准解析和更一般的 Gevrey 势的类别。