Holomorphic T-Monsters and strongly omnipresent operators

JOURNAL OF APPROXIMATION THEORY

卷:104

Article

Bernal-González, L ; Calderón-Moreno, MD

关键词: holomorphic monster;    T-monster;    strongly omnipresent operator;    infinite order differential operator;    infinite order antidifferential operator;    entire function of subexponential type;    affine linear mappings;    Laplace transform;   

DOI  :  10.1006/jath.1999.3447

来源: Elsevier

【 摘 要 】

Assume that G is a nonempty open subset of the: complex plane and that T is an operator on the linear space of holomorphic functions ill G. endowed with the compact-open topology. In this paper we introduce the notions of strongly omnipresent operator and of T-monster. which are related to the wild behaviour of certain holomorphic functions near the boundary of G. T-monsters extend a concept introduced by W.Luh and K.-G. Grosse-Erdmann. After showing that T is strongly omnipresent if and only if the set of T-monsters is residual. it is proved in this paper Ih;lt certain kinds of infinite order differential and antidifferential operators are strongly omnipresent, which improves some earlier nice results: due to the mentioned authors. (C) 2000 Academic Press.

【 授权许可】

Free