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On Pólya's Theorem in several complex variables

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Günyüz O., Zakharyuta V.

Banach Center Publications

2015

tom 107

nr 1

149-157

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.

Ograniczanie wyników

1 Banach Center Publications

1 Günyüz O.

1 Zakharyuta V.

1 2015

Wyniki wyszukiwania

On Pólya's Theorem in several complex variables