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,...
- 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
| Summary: | 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. |
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