6533b833fe1ef96bd129bfe1
RESEARCH PRODUCT
Integral holomorphic functions
Verónica DimantIgnacio ZalduendoManuel MaestrePablo Galindosubject
Mathematics::Functional AnalysisPure mathematicsGeneral MathematicsHolomorphic functional calculusMathematical analysisHolomorphic functionAnalyticity of holomorphic functionsDaniell integralCauchy's integral theoremInfinite-dimensional holomorphyIdentity theoremCauchy's integral formulaMathematicsdescription
We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Frechet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity. In this paper we define and study a class of holomorphic functions over infinite- dimensional Banach spaces admitting integral representation. Our purpose, and the motivation for our definition, are two-fold: we wish to obtain an integral repre- sentation formula akin to the Cauchy integral formula valid for some holomorphic functions over a Banach space; and we also wish to obtain a duality theorem gen- eralizing those of Sebastiao e Silva and Kothe (S), (K).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-01-01 | Studia Mathematica |