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A rigidity theorem for holomorphic generators on the Hilbert ball

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 Added by Mark Elin
 Publication date 2007
  fields
and research's language is English




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We present a rigidity property of holomorphic generators on the open unit ball $mathbb{B}$ of a Hilbert space $H$. Namely, if $finHol (mathbb{B},H)$ is the generator of a one-parameter continuous semigroup ${F_t}_{tgeq 0}$ on $mathbb{B}$ such that for some boundary point $tauin partialmathbb{B}$, the admissible limit $K$-$limlimits_{ztotau}frac{f(x)}{|x-tau|^{3}}=0$, then $f$ vanishes identically on $mathbb{B}$.



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