Assume that there are given a simply connected domain Gin the complex plane containing the open unit disk, but not the closed unit disk and an infinite triangular matrix A. Under suitable conditions on A, which are even weaker than its P-regularity, in this paper we construct a noncontinuable holomorphic function Φ on Gsuch that the A-transforms of its Taylor expansion around any point of Gtend to a scalar multiple of Φ compactly in Gand exhibit universal properties in the complement of Gwith respect to uniform approximation on compact sets and to almost everywhere approximation on measurable sets.
展开▼
