L 2-average Decay of the Fourier Transform of a Characteristic Function of a Convex Set

Alex Iosevich and Elijah Liflyand
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Alex Iosevich: University of Rochester, Department of Mathematics
Elijah Liflyand: Bar-Ilan University, Department of Mathematics

Chapter Chapter 5 in Decay of the Fourier Transform, 2014, pp 129-135 from Springer

Abstract: Abstract Let B be a bounded open set in ℝ d . As we note in the introduction, it is a consequence of the classical method of stationary phase that if $$ \partial{B} $$ is sufficiently smooth and has everywhere non-vanishing Gaussian curvature, then $$ |\hat{X}B(Rw)| \lesssim R ^{-{\frac{d+1}{2}}}$$ with constants independent of ω

Keywords: Great Circle; Convex Domain; Secant Property; Smooth Case; Analytic Number Theory (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0625-1_6

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DOI: 10.1007/978-3-0348-0625-1_6

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