We introduce an infinite-dimensional version of the classical Laplace method, in its original form, relative to a canonical Gaussian measure associated with a Hilbert space, and for a general phase function. Particular attention is given to the case of a phase function with finite-dimensional degeneracy. Explicit results on expansions in the form of power series in the relevant parameter, with estimates on remainders, are provided.

中文翻译：

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无限维高斯积分的渐近

我们介绍了经典拉普拉斯方法的无限维版本，以其原始形式，相对于与希尔伯特空间相关的规范高斯测量，以及一般相位函数。特别注意具有有限维退化的相位函数的情况。提供了在相关参数中以幂级数形式展开的明确结果，以及对余数的估计。