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UID:20260416T211940EDT-9345ValSMT@132.216.98.100
DTSTAMP:20260417T011940Z
DESCRIPTION:Title: Higher Fourier interpolation on the plane\n\nAbstract:  
 Let $lgeq 6$ be any integer\, where $lequiv 2$ mod $4$. Let $f(x)=int e^{i
 pi au |x|^2}dmu( au)$ and $mathcal{F}(f)$ be the Fourier transform of $f$\
 , where $xin R^2$ and $mu$ is a measure with bounded variation and support
 ed on a compact subset of $ au inCC$\, where $Im( au)\,Im(-rac{1}{ au})>si
 n(rac{pi}{l}).$ For every integer $kgeq 0$ and $xin R^2\,$\n	\n	We express $
 f(x)$ by the values of $rac{d^k f}{du^k}$ and $rac{d^k mathcal{F}f}{du^k}$
  at $u=rac{2n}{lambda}\,$ where $u=|x|^2$ and $lambda=2cos(rac{pi}{l}).$ W
 e show that the condition $Im( au)\,Im(-rac{1}{ au})>sin(rac{pi}{l})$ is o
 ptimal.We also identify the cokernel to these values with a specific space
  of holomorphic modular forms of weight $2k+1$ associated to the Hecke tri
 angle group $(2\,l\,infty)$.Using our explicit formulas for $l=6$ and deve
 loping new methods\, we prove a conjecture of Cohn\, Kumar\, Miller\, Radc
 henko and Viazovska~cite[Conjecture 7.5]{Maryna3} motivated by the univers
 al optimality of the hexagonal lattice.\n\nWeb details\, please contact: m
 artinez [at] crm.umontreal.ca\n
DTSTART:20210318T180000Z
DTEND:20210318T190000Z
SUMMARY:Naser Sardari (Pennsylvania State University)
URL:https://www.mcgill.ca/mathstat/channels/event/naser-sardari-pennsylvani
 a-state-university-329700
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