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A Hille-Yosida Theorem is proved on convenient vector spaces, a class, which contains all sequentially complete locally convex spaces. The approach is governed by convenient analysis and the credo that many reasonable questions concerning strongly continuous semigroups can be proved on the subspace of smooth vectors. Examples from literature are reconsidered by these simpler methods and some applications to the theory of infinite dimensional heat equations are given.

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$

Sean Dineen (1973)

Annales de l'institut Fourier

This article is devoted to a study of locally convex topologies on $H (U)$ (where $U$ is an open subset of the locally convex topological vector space $E$ and $H (U)$ is the set of all complex valued holomorphic functions on $E$ ). We discuss the following topologies on $H (U)$ :(a) the compact open topology $I_{0}$ ,(b) the bornological topology associated with $I_{0}$ ,(c) the ported topology of Nachbin $I_{ω}$ ,(d) the bornological topology associated with $I_{ω}$ ; and(e) the $I_{ω}$ topological of Nachbin.For $U$ balanced we show these topologies are...

Holomorphic germs on Banach spaces

Chae Soo Bong (1971)

Annales de l'institut Fourier

Let $E$ and $F$ be two complex Banach spaces, $U$ a nonempty subset of $E$ and $K$ a compact subset of $E$ . The concept of holomorphy type $θ$ between $E$ and $F$ , and the natural locally convex topology $𝒯_{ω, θ}$ on the vector space $ℋ_{θ} (U, F)$ of all holomorphic mappings of a given holomorphy type $θ$ from $U$ to $F$ were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space $ℋ_{θ} (K, F)$ of all germs of holomorphic mappings into $F$ around $K$ of a given holomorphy type $θ$ , and study its interplay with $ℋ_{θ} (U, F)$ and some...

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Finite-codimensional subspaces of locally convex spaces

Fixed point theorems in locally convex spaces -- the Schauder mapping method.

Fixed Points in Locally Convex Spaces.

Flache Konvexität und schwache Differenzierbarkeit.

Folgenretraktive Sequenzen lokalkonvexer Räume.

Fonctions aléatoires linéaires. Théorème de dualité

Fonctions «spline» et noyaux reproduisants d'Aronszajn-Bergman

Formes sous-linéaires minimales

Free uniform measures

Gaussian radon measures on locally convex spaces.

Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I.

Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. II.

Growth Properties of Pseudo-Convex Domains and Domains of Holomorphy in Locally Convex Topological Vector Spaces.

Hahn-Banach theorem implies Riesz theorem.

Hille-Yosida theory in convenient analysis.

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$

Holomorphic germs on Banach spaces

Hyperplanes of Locally Convex Groups

Ideales de riesz en espacios localmente k-convexos

Inductive and projective limits of $L_{p}$ spaces

Currently displaying 141 – 160 of 395