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Universality of Taylor Series as a Generic Property of Holomorphic Functions

✍ Scribed by A. Melas; V. Nestoridis

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
362 KB
Volume
157
Category
Article
ISSN
0001-8708

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✦ Synopsis

There exists a power series f 0 (z)= &=0 a & z & with radius of convergence 1, such that, for every bounded simply connected domain G, G & [z # C : |z| 1]=< and for every function f : G Γ„ C holomorphic in G ( f # H(G )), there exists a strictly increasing sequence n k # [0, 1, 2, ...] such that _ n k # n k &=0 a n k & S & (z) converges to f, as k Γ„ + , uniformly on compact subsets of G. In 1971 Chui and Parnes, independently from Luh, proved the existence of a power series &=0 a & z & with radius of convergence 1, such that, for every compact set K, K & [z # C : |z| 1]=< with K c connected and for every function h: K Γ„ C continuous on K and holomorphic in K 0 , there

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