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- W2001737369 abstract "Abstract. In this paper we study oscillatory integrals with ana-lytic homogeneous phase functions for smooth radial functions. Wegive their sharp asymptotic behavior in terms of spherical Newtondistance. 1. IntroductionIn this paper we consider oscillatory integrals I(;’) de ned byI(;’) =Z R k e if(x) ’(x)dx;where is a large positive real parameter. Here f is a homogeneouspolynomial and ’is a smooth cut-o function. In this chapter we con-sider the cases k= 2;3. Main purpose of this chapter is to reduce thedimension by one to treat the higher dimensional problems in lower di-mension. For the case k= 3 we introduce spherical Newton distance insuperadapted coordinates. A superadapted coordinate system was in-troduced by Greenblatt in [8] to describe the oscillatory index of smoothphase function in R 2 and it turned out to be a stronger notion of adaptedcoordinate system in [9].In view of the work of Varchenko [9], it is not surprising that theasymptotic behavior of I(;’) bears a close connection to the blow-upproperties of integrals of the formZ" @default.
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- W2001737369 date "2011-03-25" @default.
- W2001737369 modified "2023-10-14" @default.
- W2001737369 title "SPHERICAL NEWTON DISTANCE FOR OSCILLATORY INTEGRALS WITH HOMOGENEOUS PHASE FUNCTIONS" @default.
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- W2001737369 doi "https://doi.org/10.5831/hmj.2011.33.1.001" @default.
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