EuDML | Browse

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 Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.

Integration in function spaces and differential equations with functional derivatives

Yu. Daleckiĭ (1970)

Studia Mathematica

Interpolating discrete multiplicity varieties for $A ⁰_{p} (ℂ ⁿ)$

Bao Qin Li, Enrique Villamor (2006)

Studia Mathematica

A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space $A ⁰_{p} (ℂ ⁿ)$ .

Interpolation de fonctions analytiques bornées

Jean-Paul Bezivin (1973/1974)

Groupe de travail d'analyse ultramétrique

Interpolation d'opérateurs entre espaces de fonctions holomorphes

Patrice Lassere (1991)

Annales Polonici Mathematici

Let $K$ be a compact subset of an hyperconvex open set $D \subset ℂ^{n}$ , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to $H (D_{α})$ is a continuous...

Isometries of some F-algebras of holomorphic functions on the upper half plane

Yasuo Iida, Kei Takahashi (2013)

Open Mathematics

Linear isometries of N p(D) onto N p(D) are described, where N p(D), p > 1, is the set of all holomorphic functions f on the upper half plane D = {z ∈ ℂ: Im z > 0} such that supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.

Isomorphism of spaces of bounded continuous functions

Alain Etcheberry (1975)

Studia Mathematica

Displaying 1 – 11 of 11

Currently displaying 1 – 11 of 11