泛函分析

We consider a matrix semigroup $T: [0,\infty) \to \mathbb{R}^{d \times d}$ without assuming any measurability properties and show that, if $T$ is bounded close to $0$ and $T(t) \ge 0$ entrywise for all $t$, then $T$ is continuous. This…

The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…

In the article, the boundedness of vector-valued sublinear operators in grand variable Herz-Morrey spaces $M \dot{K}_{ \lambda, p(\cdot)}^{\eta (\cdot), q), \theta}\left(\mathbb{R}^{n}\right)$ are obtained. Then grand variable Herz-Morrey…

Generalised Morrey (function) spaces enjoyed some interest recently and found applications to PDE. Here we turn our attention to their discrete counterparts. We define generalised Morrey sequence spaces…

We generalize to Banach space Thibault-Zagrodny Theorem that if $f$ and $g$ are primal lower regular functions and $\partial f = \partial g$ locally, then $f$ and $g$ locally differ by a constant.

Rational inner functions are a generalization of finite Blaschke products to several variables. In this article we survey a variety of results about rational inner functions related to interpolation, sums of squares formulas, and boundary…

Properties of local and global slope of a function and its approximate critical points sets are studied in relation to determination of the function.

For positive $C_0$-semigroups $S$ and $T$ on a Banach lattice such that $S(t) \le T(t)$ for all times $t$, we prove that analyticity of $T$ implies analyticity of $S$. This answers an open problem posed by Arendt in 2004. Our proof is based…

In this paper we study the $L^p$ boundedness of the centred and the uncentred Hardy--Littlewood maximal operators on certain Riemannian manifolds with bounded geometry. Our results complement those of various authors. We show that, under…

We investigate the space of bounded linear operators on a Banach space equipped with a norm which is equivalent to the operator norm such that the subspace of compact operators is an M-ideal. In particular, we observe that the space of…

One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schr\"odinger equation given by \begin{equation*} \begin{cases}…

Let $\alpha>0$ and $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu,\alpha}=(\mu_{n,k,\alpha})_{n,k\ge0}$ with entries…

In this paper we study the embedding problem of an operator into a strongly continuous semigroup. We obtain characterizations for some classes of operators, namely composition operators and analytic Toeplitz operators on the Hardy space…

This paper shows how a family of function spaces (coined as Assiamoua spaces) plays a fundamental role in the Fourier analysis of vector-valued functions compact groups. These spaces make it possible to transcribe the classic results of…

We investigate when the algebraic numerical range is a $C$-spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix…

We provide a complete characterization of a subclass of weakly associative means of positive operators in the class of symmetric Kubo-Ando means. This class, which includes the geometric mean, was first introduced and studied in L.…

Let $2\leq p<\infty$ and $X$ be a complex infinite-dimensional Banach space. It is proved that if $X$ is $p$-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space…

Let $\mathcal{H}$ be a complex, separable Hilbert space, and set $\mathfrak{c}($NIL$_2)=\{ MN - NM : N, M \in \mathcal{B}(\mathcal{H}), M^2 = 0 = N^2 \}$. When $\dim\, \mathcal{H}$ is finite, we characterise the set $\mathfrak{c}($NIL$_2)$…

In this article, we study g-frames in Hilbert $C^*$-modules and investigate conditions under which the sum of two g-frames (or a g-frame and a g-Bessel sequence) remains a g-frame. We also address the stability of g-frames under certain…

This article describes Hilbert spaces contractively contained in certain reproducing kernel Hilbert spaces of analytic functions on the open unit disc which are nearly invariant under division by an inner function. We extend Hitt's theorem…