An Improved Remainder Estimate of Stationary Phase Method for Some Oscillatory Integrals over a Space of Large Dimension

MR2239911 Fujiwara, Daisuke and Kumano-go, Naoto Daisuke FUJIWARA and Naoto KUMANO-GO An Improved Remainder Estimate of Stationary Phase Method for Some Oscillatory Integrals over a Space of Large Dimension Funkcialaj Ekvacioj. Serio Internacia 49 2006 59--86 http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-1/49_59.pdf http://www.ams.org/mathscinet-getitem?mr=MR2239911 In discussing time slicing approximations of Feynman's path integrals, one can use stationary phase method for some oscillatory integrals over a space of large dimension. Previously estimates of remainder term of such stationary phase method were given in [2] and [6]. In the present note an improved remainder estimate is given for such stationary phase method. The estimate is sharp enough to give us the second term of semiclassical asymptotic expansion if it is applied to Feynman path integrals of some kind discussed in [6] and [4]. See our forthcoming paper [3]. Stationary phase method, Fourier integral operators, Feynman path integral. 81Q20, 35S30, 58D30. 49-59 2006 An Improved Remainder Estimate of Stationary Phase Method for Some Oscillatory Integrals over a Space of Large Dimension FUJIWARA, Daisuke and KUMANO-GO, Naoto Daisuke FUJIWARA and Naoto KUMANO-GO

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