On Pólya's Theorem in several complex variables

• Autorzy: Ozan Günyüz , Vyacheslav Zakharyuta
• Języki publikacji: EN

Abstrakty

EN

Let K be a compact set in ℂ, f a function analytic in ℂ̅∖K vanishing at ∞. Let $f(z) = ∑_{k=0}^{∞} a_{k}z^{-k-1}$ be its Taylor expansion at ∞, and $H_{s}(f) = det(a_{k+l})_{k,l=0}^{s}$ the sequence of Hankel determinants. The classical Pólya inequality says that
$lim sup_{s→∞} |H_{s}(f)|^{1/s²} ≤ d(K)$,
where d(K) is the transfinite diameter of K. Goluzin has shown that for some class of compacta this inequality is sharp. We provide here a sharpness result for the multivariate analog of Pólya's inequality, considered by the second author in Math. USSR Sbornik 25 (1975), 350-364.

Kategorie tematyczne

• 32A22: Nevanlinna theory (local); growth estimates; other inequalities
• 32U35: Pluricomplex Green functions
• 32A70: Functional analysis techniques \SeeMainly{}
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 107
• Numer: 1
• Strony: 149-157

Daty

wydano

2015

Twórcy

autor

Ozan Günyüz

• Sabancı University, 34956 Tuzla/İstanbul, Turkey

autor

Vyacheslav Zakharyuta

• Sabancı University, 34956 Tuzla/İstanbul, Turkey

Identyfikatory

DOI

10.4064/bc107-0-10