Related papers: H*-Normal Spaces and Some Related Functions
We investigate several boundedness properties of function spaces considered as uniform spaces.
The study of infra-topological spaces focuses on characterizations of $e^\star$-open sets and nearby open sets in infra-topological spaces. The $e^\star$-open sets, a variation of open sets, are explored for their unique properties and…
Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.
In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…
We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called associated weight function where the weight(system) is…
The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…
We develop some nonstandard techniques for bornological and coarse spaces. We first generalise the notion of bornology to prebornology, which better fits to coarse spaces. We then give nonstandard characterisations of some basic large-scale…
The $L^{p,\infty}$ quasi-norm of functions on a measure space can be characterized in terms of their pairing with normalized characteristic functions. We generalize this result to the case of the outer $L^{p,\infty}$ quasi-norms for…
The article is devoted to investigation of classes of functions monotone as functions on general $C^*$-algebras that are not necessarily the $C^*$-algebras of all bounded linear operators on a Hilbert space as it is in classical case of…
Here we have introduced and studied the idea of $ Ig^*$-closed set with respect to an ideal and investigated some of its properties in Alexandroff spaces. We have also introduced $ Ig^*$-$T_0 $ axiom, $ Ig^*$-$T_1$ axiom, $ Ig^*$-$T_\omega…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…
In this paper we study the idea of strong-I^K-convergence of functions which is common generalization of strong-I*-convergence of functions in probabilistic metric spaces. We also study strong-I^K-limit points of functions in the same…
In this paper we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames on Hilbert spaces. Moreover, we define the related oprators of c-K-g…
Let ${\mathcal X}$ be an RD-space, which means that ${\mathcal X}$ is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in ${\mathcal X}$. In this paper, the…
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit…
In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…
We define a very general notion of regularity for functions taking values in an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over…
The aim of this paper is to introduce and study the concept of a contra-semicontinuous function and further investigate the class of strongly $S$-closed spaces. We obtain some new decompositions of generalized continuous functions.