2014 | OriginalPaper | Chapter
Average Decay Estimates for Fourier Transforms of Measures Supported on Curves
Authors : Alex Iosevich, Elijah Liflyand
Published in: Decay of the Fourier Transform
Publisher: Springer Basel
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The previous three chapters dealt with average decay for subsets of ℝ
d
, which quickly reduces to the problem of average decay of Fourier transforms of measures supported on surfaces of co-dimension one. In this chapter we address the issue of Fourier transform of average decay of measures supported on curves in ℝ
d
with some tantalizing connection with the classical restriction theory.