关于超曲面上测度的Fourier变换的零点  

About the Null Set of the Fourier Transform for a Surface Carried Measure

作　　者：孙利民[1] 

机构地区：[1]杭州大学数学系

出　　处：《数学学报（中文版）》1995年第1期1-5,共5页Acta Mathematica Sinica：Chinese Series

摘　　要：设Ｓ是Ｅｕｃｌｉｄ空间Ｒ￣ｎ（ｎ≥２）中一个紧闭光滑超曲面，它关于原点中心对称，其Ｇａｕｓｓ曲率处处非零。设ｄμ是Ｓ上一个光滑正测度，是其Ｆｏｕｒｉｅｒ变换。本文证明，的零点集是一个紧集与可列多个微分同胚于单位球面的超曲面之无交并．Let S R￣n(n≥2)be a compact smooth hypersurface without boundary. Assumethat S is centrally symmetric with respect to the origin,and that the Gaussian curvature of S isnon-zero. Let dμ be a smooth positive measure on S,and dμ be the Fourier transform of dμ,Weshow that the null set of is a disjoint union of a compact set and countably many hyper-surfaceswhich are all diffemorphic to S￣(n-1)。

关 键 词：超曲面 零点 测度 傅里叶变换 

分 类 号：O174.22[理学—数学]