On the topological description of weighted inductive limits of spaces of holomorphic and harmonic functions

1999 ◽  
Vol 72 (5) ◽  
pp. 360-366 ◽  
Author(s):  
Jos� Bonet ◽  
Dietmar Vogt
Keyword(s):  
Harmonic Functions ◽  
Inductive Limits ◽  
Topological Description ◽  
Weighted Inductive Limits

scholarly journals On weighted inductive limits of spaces of ultradifferentiable functions and their duals

2018 ◽  
Vol 292 (3) ◽  
pp. 573-602 ◽  
Author(s):  
Andreas Debrouwere ◽  
Jasson Vindas
Keyword(s):  
Inductive Limits ◽  
Ultradifferentiable Functions ◽  
Weighted Inductive Limits

scholarly journals The subspace problem for weighted inductive limits of spaces of holomorphic functions.

1995 ◽  
Vol 42 (2) ◽  
pp. 259-268 ◽  
Author(s):  
José Bonet ◽  
Jari Taskinen
Keyword(s):  
Holomorphic Functions ◽  
Inductive Limits ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Inductive Limits ◽  
Subspace Problem

On weighted inductive limits of spaces of continuous functions

1986 ◽  
Vol 192 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Jos� Bonet
Keyword(s):  
Continuous Functions ◽  
Inductive Limits ◽  
Spaces Of Continuous Functions ◽  
Weighted Inductive Limits

scholarly journals PROJECTIVE DESCRIPTION OF WEIGHTED (LF)-SPACES OF HOLOMORPHIC FUNCTIONS ON THE DISC

2003 ◽  
Vol 46 (2) ◽  
pp. 435-450 ◽  
Author(s):  
Klaus D. Bierstedt ◽  
José Bonet
Keyword(s):  
Double Sequence ◽  
Holomorphic Functions ◽  
Growth Conditions ◽  
Inductive Limits ◽  
Primary 46E10 ◽  
Secondary 30H05 ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Inductive Limits ◽  
Projective Description ◽  
Necessary And Sufficient

AbstractThe topology of certain weighted inductive limits of Fréchet spaces of holomorphic functions on the unit disc can be described by means of weighted sup-seminorms in case the weights are radial and satisfy certain natural assumptions due to Lusky; in the sense of Shields and Williams the weights have to be normal. It turns out that no assumption on the (double) sequence of normal weights is necessary for the topological projective description in the case of o-growth conditions. For O-growth conditions, we give a necessary and sufficient condition (in terms of associated weights) for projective description in the case of (LB)-spaces and normal weights. This last result is related to a theorem of Mattila, Saksman and Taskinen.AMS 2000 Mathematics subject classification: Primary 46E10. Secondary 30H05; 46A13; 46M40

scholarly journals Weighted spaces of harmonic and holomorphic functions: sequence space representations and protective descriptions

1997 ◽  
Vol 40 (1) ◽  
pp. 41-62 ◽  
Author(s):  
Päivi Mattila ◽  
Eero Saksman ◽  
Jari Taskinen
Keyword(s):  
Unit Disk ◽  
Harmonic Functions ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Open Unit ◽  
Open Unit Disk ◽  
Inductive Limits ◽  
Complemented Subspaces ◽  
Bounded Functions ◽  
Köthe Sequence Spaces

We study the structure of inductive limits of weighted spaces of harmonic and holomorphic functions defined on the open unit disk of ℂ, and of the associated weighted locally convex spaces. Using a result of Lusky we prove, for certain radial weights on the open unit disk D of ℂ, that the spaces of harmonic and holomorphic functions are isomorphic to complemented subspaces of the corresponding Köthe sequence spaces. We also study the spaces of harmonic functions for certain non-radial weights on D. We show, under a natural sufficient condition for the weights, that the spaces of harmonic functions on D are isomorphic to corresponding spaces of continuous or bounded functions on ∂D.

Weighted Inductive Limits of Holomorphic Functions with o-Growth Condition

2018 ◽  
Vol 13 (2) ◽  
pp. 341-349
Author(s):  
Alexander V. Abanin ◽  
Pham Trong Tien
Keyword(s):  
Growth Condition ◽  
Holomorphic Functions ◽  
Inductive Limits ◽  
Weighted Inductive Limits

scholarly journals A projective description of weighted inductive limits

1982 ◽  
Vol 272 (1) ◽  
pp. 107-107 ◽  
Author(s):  
Klaus-D. Bierstedt ◽  
Reinhold Meise ◽  
William H. Summers
Keyword(s):  
Inductive Limits ◽  
Weighted Inductive Limits ◽  
Projective Description
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