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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$L^{2}$ asymptotes for Fourier transforms of surface- carried measures


Author: Stuart Nelson
Journal: Proc. Amer. Math. Soc. 28 (1971), 134-136
MSC: Primary 42.25
DOI: https://doi.org/10.1090/S0002-9939-1971-0283491-0
MathSciNet review: 0283491
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Abstract: W. Littman has shown how to obtain asymptotic approximations for Fourier transforms of surface-carried measures of the form $\mu (X)dA$ where $dA$ represents the area measure for the surface as a subset of Euclidean space and $\mu (X)$ is a compactly supported ${C^\infty }$ function. Here we extend to the case where $\mu (X)$ is an ${L^2}$ function.


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Keywords: Multi-variable Fourier transform, asymptotic approximation, Gaussian curvature, Parseval’s equality, <IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${L^2}$"> asymptotes, surface-carried measure
Article copyright: © Copyright 1971 American Mathematical Society