Dimitri Gioev
Published 2002-12-18, updated 2007-06-29Version 3
We study inequalities between general integral moduli of continuity of a function and the tail integral of its Fourier transform. We obtain, in particular, a refinement of a result due to D. B. H. Cline [2] (Theorem 1.1 below). We note that our approach does not use a regularly varying comparison function as in [2]. A corollary of Theorem 1.1 deals with the equivalence of the two-sided estimates on the modulus of continuity on one hand, and on the tail of the Fourier transform, on the other (Corollary 1.5). This corollary is applied in the proof of the violation of the so-called entropic area law for a critical system of free fermions in [4,5].
Comments: 15 pages, 1 figure, case of dim=1 added, to appear in: Integable systems, random matrices, and applications: Conference in honor of Percy Deift's 60th birthday (New York, NY, 2006), Contemp. Math., Amer. Math. Soc
On the Fourier Transform of Bessel Functions over Complex Numbers - I: the Spherical Case
On an apparently bilinear inequality for the Fourier transform
On the Fourier transform of function of two variables which depend only on the maximum of these variables
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