科研之友
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摘要
For a holomorphic function f in the unit disk, S-n(f) denotes the n-th partial sum of the Taylor development of f with center at 0. We show that given a strictly increasing sequence of positive integers (A.), there exists a holomorphic function f on the unit disk such that the pairs of partial sums {(S-n(f), S-lambda n(f)) : n = 1, 2,...} approximate all plausibly approximable functions uniformly on suitable compact subsets K of the complex plane if and only if lim sup(n) lambda(n)/n= +infinity. This provides a new strong notion of universality for Taylor series.
- 出版日期2014-3
