BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Angel Kumchev (Towson University)
DTSTART:20200603T133000Z
DTEND:20200603T135500Z
DTSTAMP:20260423T011218Z
UID:CANT2020/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/30/
 ">Bounds for discrete maximal functions of codimension 3</a>\nby Angel Kum
 chev (Towson University) as part of Combinatorial and additive number theo
 ry (CANT 2021)\n\n\nAbstract\nWe study the bilinear discrete averaging ope
 rator \n$T_{\\lambda}(f\,g)(x) = \\sum_{m\,n \\in V_{\\lambda}}  f(x-m) g(
 x-n)$\, \nwhere $f$ and $g$ are functions in $\\ell^p(\\mathbb Z^d)$ and $
 \\ell^q(\\mathbb Z^d)$ \nand the summation is over the integer solutions $
 (m\,n) \\in \\mathbb Z^{2d}$ of the equations \n\\[ |m|^2 = |n|^2 = 2m \\c
 dot n = \\lambda\, \\]\nwhere $|\\cdot|$ is the standard Euclidean norm on
  $\\mathbb R^d$.  \nWe prove an approximation formula for the Fourier mult
 iplier of $T_{\\lambda}$ \nand establish the boundedness of the respective
  maximal operator \nfrom $\\ell^p(\\mathbb Z^d \\times \\ell^q(\\mathbb Z^
 d)$ to $\\ell^r(\\mathbb Z^d)$ \nfor a range of choices for $p\,q\,r$. Our
  work is related to classical work on simultaneous \nrepresentations of in
 tegers by quadratic forms as well as to the study \nof point configuration
 s in combinatorial geometry. \n\nJoint work with T.C. Anderson and E.A. Pa
 lsson.\n
LOCATION:https://researchseminars.org/talk/CANT2020/30/
END:VEVENT
END:VCALENDAR