On some spaces of analytic functions and their duality relations

For each 0 ≤ C   and lt; + ∞and 0 and lt; p and lt; +∞ let EC,p be the space of entire functions f such that, for some constant A  ≥ 0,|f(z) ≤  AeC|z|p for all z in c. If ||f|| C, p is the minimun of such constants A, ||  ||c,p is a Banach space norm on EC,p.Let 0 and lt; B ≤ + ∞ and denote with EB, p the inductive limit space of the Banach spaces EC,p , 0 ≤  C and lt; B. The topological dual space of EB, p is identified as the space 0B,p of analytic functions on the open disk D(0,(Bp)1/p). If 0B,P is given the topology of uniform convergence on compact sets, its topological dual is also identified as EB,p. Relations between different topologies on the spaces EC,p and EB, p having their origin in the duality are also examinea.

• Autores: Charris Castañeda, Jairo Antonio; Huérfano, Ruth S.
• Tipo de recurso: Article of journal
• Fecha de publicación: 1988
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/43214
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/43214; http://bdigital.unal.edu.co/33312/
• Palabra clave: Entire functions; Banach space; space race; inductive Banach dual topological space; analytic functions; open disk; topology convergence compact sets; different topologies
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional