Related papers: The Real-Valued Bochner integral and the Modern Re…

In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable…

In this paper we introduce an equivalence relation on the classes of almost periodic functions of a real or complex variable which is used to refine Bochner's result that characterizes these spaces of functions. In fact, with respect to the…

We consider the space (weighted Fourier algebra) of Banach algebra valued functions $A^q_{\omega}(\Gamma,\cX),$ which consists of all Fourier transforms of functions in $L^q_\omega(G,\cX)$. Here $\omega$ is a Beurling-Domar type weight on a…

We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To…

On any proper convex domain in real projective space there exists a natural Riemannian metric, the Blaschke metric. On the other hand, distances between points can be measured in the Hilbert metric. Using techniques of optimal control, we…

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a…

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

The aim of this article is to study effective Reifenberg theorems for measures in a Hilbert or Banach space. For Hilbert spaces, we see all the results from $\mathbb{R}^n$ continue to hold with no additional restrictions. For a general…

Classification theorems for linear differential equations in two real variables, possessing eigenfunctions in the form of the polynomials (the generalized Bochner problem) are given. The main result is based on the consideration of the…

Given a Hilbert space $\mathcal H$ and a finite measure space $\Omega$, the approximation of a vector-valued function $f: \Omega \to \mathcal H$ by a $k$-dimensional subspace $\mathcal U \subset \mathcal H$ plays an important role in…

We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…

We demonstrate the necessity of a Poincar\'e type inequality for those metric measure spaces that satisfy Cheeger's generalization of Rademacher's theorem for all Lipschitz functions taking values in a Banach space with the Radon-Nikodym…

Let $X\left(\mathbb{R}^{n}\right)$ be a ball quasi-Banach function space on $\mathbb{R}^{n}$, $WX\left(\mathbb{R}^{n}\right)$ be the weak ball quasi-Banach function space on $\mathbb{R}^{n}$, $H_{X}\left(\mathbb{R}^{n}\right)$ be the Hardy…

In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_X$ of a complex Banach space $X$ into $\mathbb{C}$. As applications, we will establish refined Bohr…

UNIFORM algebras have been extensively investigated because of their importance in the theory of uniform approximation and as examples of complex Banach algebras. An interesting question is whether analogous algebras exist when a complete…

Integrally convex functions constitute a fundamental function class in discrete convex analysis. This paper shows that an integer-valued integrally convex function admits an integral subgradient and that the integral biconjugate of an…

This paper explores some important aspects of the theory of rearrangement-invariant quasi-Banach function spaces. We focus on two main topics. Firstly, we prove an analogue of the Luxemburg representation theorem for rearrangement-invariant…

In this paper, we define the Dunford-Henstock-Kurzweil and the Dunford-McShane integrals of Banach space valued functions defined on a bounded Lebesgue measurable subset of m-dimensional Euclidean space Rm. We will show that the new…

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…

Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…