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SUMMARY:Yuanpu Xiong (Tonji University)
DTSTART:20261023T140000Z
DTEND:20261023T150000Z
DTSTAMP:20261026T214404Z
UID:OARS/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/82/">On
  the removable singularities of $L^2$ holomorphic functions</a>\nby Yuanpu
  Xiong (Tonji University) as part of OARS Online Analysis Research Seminar
 \n\n\nAbstract\nLet $\\Omega$ be a domain in $\\mathbb{C}$ and $E$ a close
 d subset of $\\Omega$. Carleson proved that if $E$ has zero logarithmic ca
 pacity\, then any $L^2$ holomorphic function on $\\Omega\\setminus E$ can 
 be holomorphically extended to $\\Omega$. In particular\, the Bergman kern
 el on $\\Omega$ coincides with the Bergman kernel on $\\Omega\\setminus E$
 . In this talk\, I will discuss the case where $E$ has small logarithmic c
 apacity\, and introduce an absolutely continuous property of the Bergman k
 ernel\, which also leads to a proof of Carleson's theorem.\n
LOCATION:https://researchseminars.org/talk/OARS/82/
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