Related papers: Characteristic functions as bounded multipliers on…

In this paper, we extend some recent results of Guedj-Lu-Zeriahi about psh envelopes of bounded functions on bounded domains in $\mathbb{C}^n$. We also present a result on the regularity of psh envelopes.

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…

Let $(C(t))\_{t \in R}$ be a cosine function in a unital Banach algebra. We show that if $sup\_{t\in R}\Vert C(t)-cos(t)\Vert \textless{} 2$ for some continuous scalar bounded cosine function $(c(t))\_{t\in \R},$ then the closed subalgebra…

We study unboundedness properties of functions belonging to generalised Morrey spaces ${\mathcal M}_{\varphi,p}({\mathbb R}^d)$ and generalised Besov-Morrey spaces ${\mathcal N}^{s}_{\varphi,p,q}({\mathbb R}^d)$ by means of growth…

In this paper we establish $L^p$-boundedness properties for Laplace type transform spectral multipliers associated with the Schr\"odinger operator $\mathcal{L}=-\Delta +V$. We obtain for this type of multipliers pointwise representation as…

We prove in this paper that a sequence $M:\mathbb{Z}^{n}\to\mathcal{L}(E)$ of bounded variation is a Fourier multiplier on the Besov space $B_{p,q}^{s}(\mathbb{T}^{n},E)$ for $s\in\mathbb{R}$, $1<p<\infty$, $1\leq q\leq\infty$ and $E$ a…

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…

We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.

Given a smooth bounded planar domain, we construct a compact set on the boundary s.t. its characteristic function is not the trace of a least gradient function. This generalize the construction of Spradlin and Tamasan [ST14] on the disc.

The purpose of this paper is to provide some properties of maximal plurisubharmonic functions in a bounded domain of \mathbb{C}^n

The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…

In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of these spaces are established along with applications to…

For various function spaces of the form gU or U+gV, U and V e.g. almost periodic functions AP, (bounded) uniformly continuous functions BUC, UC, g(t) = exp(it^2), their properties are discussed, especially a Loomis type condition (Delta)…

We provide a few characterizations of a strictly convex Banach space. Using this we improve the main theorem of [Digar, Abhik; Kosuru, G. Sankara Raju; Cyclic uniform Lipschitzian mappings and proximal uniform normal structure. Ann. Funct.…

Given a compact space $X$ and a commutative Banach algebra $A$, the character spaces of $A$-valued function algebras on $X$ are investigated. The class of natural $A$-valued function algebras, those whose characters can be described by…

Let $\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty$. Let $\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty$. Define $\acn$ to…

We prove a commutative Gelfand--Naimark type theorem, by showing that the set $C_s(X)$ of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space $X$ (provided with the supremum…

The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.

We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in…