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RESEARCH PRODUCT
Spaces of holomorphic functions in regular domains
Manuel Valdiviasubject
Pure mathematicsExtensions of holomorphic functionsRegular complex domainsDense-lineabilityLinear spaceApplied MathematicsMathematical analysisHolomorphic functionZero (complex analysis)Linear subspaceDomain (mathematical analysis)Fréchet spaceBounded functionComplex planeAnalysisMathematicsdescription
AbstractLet Ω be a regular domain in the complex plane C, Ω≠C. Let Gb(Ω) be the linear space over C of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure Ω¯ of Ω, n=0,1,2,… . We endow Gb(Ω), in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of Gb(Ω), with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-02-01 | Journal of Mathematical Analysis and Applications |