Oscillatory integral with polynomial phase

Abstract

Oscillatory integral of the form ε e i(x·u+tP(x)) ∝(x)dx is discussed in this paper; type of critical point of a polynomial is introduced; asymptotic behaviour of the oscillatory integral is given; finally, a restriction theorem of Fourier Transform on algebraic hypersurface (x1, x2, ..., x n , P(x)) is obtained as an application.KeywordsDifferential OperatorRestriction TheoremUnit BallCompact SupportElliptic CurveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.