We give a unified approach to handle the problem of extending functions with values in locally convex Hausdorff space $E$ over field $\mathbb{K}$, which have weak extensions $\mathcal{F}(\Omega,\mathbb{K})$ scalar-valued on set $\Omega$, vector-valued counterpart $\mathcal{F}(\Omega,E)$ $\mathcal{F}(\Omega,\mathbb{K})$. The results obtained are based upon representation as linear continuous ope...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

We consider the valued fieldK := R((Γ)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a derivat...

We consider the valued field K := R((Γ)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

We consider the valued field K := R((Γ)) of generalized series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.

Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T lZ2 (Received June 30, 1992 and in revised form November 7, 1992) ABSTRACT. A formula is set up between vector-vMued mean and scMax-valued that enbles translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-vMued means, .how tha...