BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (University of Birmingham)
DTSTART:20200512T153000Z
DTEND:20200512T163000Z
DTSTAMP:20260404T121953Z
UID:LisbonWADE/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LisbonWADE/4
 /">Global maximizers for spherical restriction</a>\nby Diogo Oliveira e Si
 lva (University of Birmingham) as part of Lisbon webinar in analysis and d
 ifferential equations\n\n\nAbstract\nWe prove that constant functions are 
 the unique real-valued maximizers for all $L^2-L^{2n}$ adjoint Fourier res
 triction inequalities on the unit sphere $\\mathbb{S}^{d-1}\\subset\\mathb
 b{R}^d$\, $d\\in\\{3\,4\,5\,6\,7\\}$\, where $n\\geq 3$ is an integer. The
  proof uses tools from probability theory\, Lie theory\, functional analys
 is\, and the theory of special functions. It also relies on general soluti
 ons of the underlying Euler--Lagrange equation being smooth\, a fact of in
 dependent interest which we discuss. We further show that complex-valued m
 aximizers coincide with nonnegative maximizers multiplied by the character
  $e^{i\\xi\\cdot\\omega}$\, for some $\\xi$\, thereby extending previous w
 ork of Christ & Shao (2012) to arbitrary dimensions $d\\geq 2$ and general
  even exponents. This talk is based on results obtained with René Quilodr
 án.\n
LOCATION:https://researchseminars.org/talk/LisbonWADE/4/
END:VEVENT
END:VCALENDAR