The Laplace transform of analytic vector-valued functions (real conditions)

Growth and Range Conditions for the Laplace Representation of Vector-valued Functions

Laplace Transform of Distribution-valued Functions and Its Applications

1. Notation and notions We repeat some definitions and facts, we need in our exposition but for special case. Let Q be an open set belonging to Rn. By D(Q) we denote the space {φ ∈ C∞(Q); suppφ ⊂ Kφ}, Kφ is a compact set in Q which depends on φ. D′(Q) is the space of continuous linear functionals on D(Q) the space of distributions. Every f ∈ Lloc(Q) defines a distribution, called regular distri...

The ring of real-valued functions on a frame

In this paper, we define and study the notion of the real-valued functions on a frame $L$. We show that $F(L) $, consisting of all frame homomorphisms from the power set of $mathbb{R}$ to a frame $ L$, is an $f$-ring, as a generalization of all functions from a set $X$ into $mathbb R$. Also, we show that $F(L) $ is isomorphic to a sub-$f$-ring of $mathcal{R}(L)$, the ring of real-valued continu...

Vector - Valued Weakly Analytic

Pointfree topology version of image of real-valued continuous functions

Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...