Boundary Behavior of Universal Taylor Series and Their Derivatives |
| |
| Authors: | David H Armitage George Costakis |
| |
| Institution: | (1) Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom;(2) University of Edinburgh, School of Mathematics, James Clerk Maxwell Building, King's Buildings, Edinburgh EH9 3JZ, Scotland, United Kingdom; Current address: University of Crete, Department of Mathematics, Knossu Avenue, GR-714 09, Heraklion, Crete, Greece |
| |
| Abstract: | For a given first category subset E of the unit
circle and any given holomorphic function g on the open unit
disk, we construct a universal Taylor series f on the open unit
disk, such that, for every n = 0,1,2,..., f(n) is close to
g(n) on a set of radii having endpoints in E. Therefore,
there is a universal Taylor series f, such that f and all its
derivatives have radial limits on all radii with endpoints in E.
On the other hand, we prove that if f is a universal Taylor
series on the open unit disk, then there exists a residual set G
of the unit circle, such that for every strictly positive integer
n, the derivative f(n) is unbounded on all radii with
endpoints in the set G. |
| |
| Keywords: | Taylor series Collingwood maximality theorem Mergelyan's approximation theorem |
| 本文献已被 SpringerLink 等数据库收录！ |
|
