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SUMMARY:Diogo Oliveira e Silva (Instituto Superior Técnico Lisboa)
DTSTART:20230308T170000Z
DTEND:20230308T180000Z
DTSTAMP:20260423T052644Z
UID:HAeS/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HAeS/42/">Ex
 ponentials rarely maximize Fourier extension inequalities for cones</a>\nb
 y Diogo Oliveira e Silva (Instituto Superior Técnico Lisboa) as part of H
 armonic analysis e-seminars\n\n\nAbstract\nThis talk is based on recent jo
 int work with G. Negro\, B. Stovall and J. Tautges.\nGlobal maximizers for
  the $L^2$ Fourier extension inequality on the cone in $\\mathbb R^{1+d}$ 
 have been characterized in the lowest-dimensional cases $d\\in\\{2\,3\\}$.
  We prove that these functions are critical points for the $L^p$ to $L^q$ 
 Fourier extension inequality if and only if $p=2$. We also establish the e
 xistence of maximizers and the precompactness of $L^p$-normalized maximizi
 ng sequences modulo symmetries for all valid scale-invariant Fourier exten
 sion inequalities on the cone in $\\mathbb R^{1+d}$. In the range for whic
 h such inequalities are conjectural\, our result is conditional on the bou
 ndedness of the extension operator. The proof uses tools from the calculus
  of variations\, bilinear restriction theory\, conformal geometry and the 
 theory of special functions.\n
LOCATION:https://researchseminars.org/talk/HAeS/42/
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