On the relation between maximum modulus, maximum term, and Taylor coefficients of an entire function
نویسندگان
چکیده
منابع مشابه
Maximum Modulus, Maximum Term and Interpolation Error of an Entire Function
Let f be analytic on the compact set E ⊂ C , of positive transfinite diameter and let Cr denote the largest equipotential curve of E such that f is analytic within Cr. Generally, the growth of an entire function is measured in terms of its order and type. Here we have established the relations between maximum modulus, maximum term and interpolation error of best uniform approximation to a funct...
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Let f(z) := ∑n ν=0 aνz ν be a polynomial of degree n having no zeros in the open unit disc, and suppose that max|z|=1 |f(z)| = 1. How small can max|z|=ρ |f(z)| be for any ρ ∈ [0 , 1)? This problem was considered and solved by Rivlin [4]. There are reasons to consider the same problem under the additional assumption that f ′(0) = 0. This was initiated by Govil [2] and followed up by the present ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1985
ISSN: 0021-9045
DOI: 10.1016/0021-9045(85)90127-3