Stationary Phase Method with an Estimate of the Remainder Term over a Space of Large Dimension

Stationary phase method is a method to evaluate asymptotically, as ν → ∞, oscillatory integrals over R^d of the following form: I ( S , a , ν ) = ∫ R d e − i ν S ( x ) a ( x ) d x , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072096/6e6221c8-364d-4a5e-bfe5-98bb034e69b7/content/eq1.tif"/>