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Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ is generated by a quasi-inner function, we also provide relationships of…
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear…
We introduce and analyze spaces and algebras of generalized functions which correspond to H\" older, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are…
We characterize the valuations on the space of quasi-concave functions defined on the $N$-dimensional Euclidean space, that are rigid motion invariant and continuous with respect to a suitable topology. Among them we also provide a specific…
A function $f$ on a topological space is sequentially continuous at a point $u$ if, given a sequence $(x_{n})$, $\lim x_{n}=u$ implies that $\lim f(x_{n})=f(u)$. This definition was modified by Connor and Grosse-Erdmann for real functions…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to the setting of solid BF-spaces as it is…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
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…
Extrinsic and intrinsic characterizations are given for the class DSC(K) of differences of semi-continuous functions on a Polish space K, and also decomposition characterizations of DSC(K) and the class PS(K) of pointwise stabilizing…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$. A companion survey provides equivalent definitions and basic…
A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…
Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are determined in a rigid form but any minimal cells can…
The purpose of this study is to introduce a new class of regular spaces called e*$\theta$-regular spaces which is a generalization of the class of $\beta\theta$-regular spaces. Also, we investigate some basic properties and several…
A function $f$ defined on a 2-normed space $ (X,||.,.||)$ is ward continuous if it preserves quasi-Cauchy sequences where a sequence $(x_n)$ of points in $X$ is called quasi-Cauchy if $lim_{n\rightarrow\infty}||\Delta x_{n},z||=0$ for every…
We study notions of absolute continuity for functions defined on $\mathbb{R}^n$similar to the notion of $\alpha$-absolute continuity in the sense of Bongiorno. We confirm a conjecture of Mal\'y that 1-absolutely continuous functions do not…
In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we…