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- W2064657871 abstract "Let B n r ={z ϵ C n :¦z¦<r} , where ¦·¦ is the Euclidean norm, and for X ⊂ C n , let H X denote the closed convex hull of X in C n . In 1990, Graham showed that if f is a normalized holomorphic map from B n 1 into C n , and if f is either an open map or a polynomial map, then there is a sharp, uniform constant a , a given by ae 1+ a =1, such that H f ( B n 1 ) ⊃ B n a . Graham posed the question to find, for normalized polynomial maps f of degree m , the best constant a m so that H f ( B n 1 ) ⊃ B n a m . We answer this question and obtain, for each m , the sharp constant a m =a+ a ln m 2(1+a)m + a ln { 2π (1+a)/a} (1+a)m + 1 m , m→ ∞ We also note that this solution extends an old result of Pólya and Szegő." @default.
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- W2064657871 date "1993-06-01" @default.
- W2064657871 modified "2023-09-29" @default.
- W2064657871 title "An application from partial sums of ez to a problem in several complex variables" @default.
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- W2064657871 doi "https://doi.org/10.1016/0377-0427(93)90301-q" @default.
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