The stationary phase method with an estimate of the remainder term on a space of large dimension

Abstract

In discussing convergence of Feynman path integrals [2], we need a stationary phase method of oscillatory integrals over a space of large dimension. More precisely, we have to know how the remainder term behaves when the dimension of the space goes to ∞ (cf. [2], [3] and [5]). The aim of the present note is to give answer to this question under rather mild assumptions. Application to the Feynman path integrals is discussed in [3] and [5].