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SUMMARY:Discrete temperate distributions in Euclidean spaces
DTSTART;VALUE=DATE-TIME:20210703T135500Z
DTEND;VALUE=DATE-TIME:20210703T142500Z
DTSTAMP;VALUE=DATE-TIME:20260418T035323Z
UID:indico-contribution-190@indico.eimi.ru
DESCRIPTION:Speakers: Sergii Favorov (Karazin's Kharkiv national universit
 y)\nLet  $f=\\sum_{\\lambda\\in\\Lambda}\\sum_k p_k(\\lambda) D^k\\delta_\
 \lambda$ be a temperate distribution on $\\mathbb{R}^d$ with uniformly dis
 crete support $\\Lambda$ and uniformly discrete spectrum (that is $supp\\h
 at f$). We prove that under conditions\n$$\n    0 < c\\le\\sum_k|p_k(\\lam
 bda)|\\le C < \\infty\n$$\nthe support $\\Lambda$ is a finite union of cos
 ets of full-rank lattices. The optimality of the above estimates is discus
 sed. The result generalizes the corresponding one for discrete measures [1
 ]. For its proof we use some properties of almost periodic distributions a
 nd a local version of Wiener's Theorem on trigonometric series.\n\n[1]  S.
 Yu.Favorov\, *Large Fourier Quasicrystals and Wiener's Theorem*\,  Journal
  of Fourier Analysis and Applications\, Vol. 25\, Issue 2\, (2019)\, 377-3
 92.\n\nhttps://indico.eimi.ru/event/321/contributions/190/
LOCATION:
URL:https://indico.eimi.ru/event/321/contributions/190/
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