Turkish Journal of Mathematics
DOI
-
Abstract
We consider hypersurfaces S \subset \RR^3 with zero Gaussian curvature at every ordinary point with surface measure dS and define the surface measure d\mu = \psi(x)dS(x) for smooth function \psi with compact support. We obtain uniform estimates for the Fourier transform of measures concentrated on such hypersurfaces. We show that due to the damping effect of the surface measure the Fourier transform decays faster than O( \xi ^{-1/h}), where h is the height of the phase function. In particular, Fourier transform of measures supported on the exceptional surfaces decays in the order O( \xi ^{-1/2}) (as \xi \to +\infty).
Keywords
Oscillatory Integrals, oscillation index, singular hypersurfaces, curvature
First Page
1
Last Page
21
Recommended Citation
IKROMOV, ISROIL A. (2007) "Estimates for Fourier Transform of Measures Supported on Singular Hypersurfaces," Turkish Journal of Mathematics: Vol. 31: No. 1, Article 1. Available at: https://journals.tubitak.gov.tr/math/vol31/iss1/1
