An internal polya inequality for ℂ-convex domains in ℂ n

Günyüz, Ozan and Zakharyuta, Vyacheslav (2019) An internal polya inequality for ℂ-convex domains in ℂ n. Mathematical Notes, 105 (3-4). pp. 351-358. ISSN 0001-4346 (Print) 1573-8876 (Online)

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Let K ⊂ ℂ be a polynomially convex compact set, f be a function analytic in a domain ℂ¯ \ K with Taylor expansion f(z)=∑k=0∞ak/zk+1 at ∞, and Hi(f):=det(ak+l)k,l=0i be the related Hankel determinants. The classical Polya theorem [11] says that lim supi→∞|Hi(f)|1/i2≤d(K), where d(K) is the transfinite diameter of K. The main result of this paper is a multivariate analog of the Polya inequality for a weighted Hankel-type determinant constructed from the Taylor series of a function analytic on a ℂ-convex (= strictly linearly convex) domain in ℂ n .
Item Type: Article
Uncontrolled Keywords: Polya inequality; transfinite diameter; ℂ-convexity
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Ozan Günyüz
Date Deposited: 22 Jul 2023 16:30
Last Modified: 22 Jul 2023 16:30

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