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Abstrakty
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.
$lim sup_{s→∞} |H_{s}(f)|^{1/s²} ≤ d(K)$,
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
149-157
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
- Sabancı University, 34956 Tuzla/İstanbul, Turkey
autor
- Sabancı University, 34956 Tuzla/İstanbul, Turkey
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-10