Related papers: Shape preserving properties of generalized Bernste…

In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always…

We describe the structure of the bijective transformations on the set of density operators which preserve the Bregman $f$-divergence for an arbitrary differentiable strictly convex function $f.$ Furthermore, we determine the preservers of…

Let $U\subseteq\mathbb{R}^{n}$ be open and convex. We show that every (not necessarily Lipschitz or strongly) convex function $f:U\to\mathbb{R}$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we…

This paper is concerned with a boundedness of trace and extension operators for Besov spaces and Triebel-Lizorkin spaces on upper half space with variable exponents. To define trace and extension operators, we introduce a quarkonial…

The article examines Nikolskii and Besov spaces with norms defined using $L_p$-averaged mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative…

We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and…

Recently, Kulikov (\cite{Ku}) has shown that certain convex functionals on weighted Bergman spaces are maximized by reproducing kernels. We show a sharp quantitative stability of these estimates with the optimal norm and the exponent and an…

Denote by $M_n$ the set of $n\times n$ complex matrices. Let $f: M_n \rightarrow [0,\infty)$ be a continuous map such that $f(\mu UAU^*)= f(A)$ for any complex unit $\mu$, $A \in M_n$ and unitary $U \in M_n$, $f(X)=0$ if and only if $X=0$…

We provide new sufficient conditions for Chebyshev estimates for Beurling generalized primes. It is shown that if the counting function $N$ of a generalized number system satisfies the $L^{1}$-condition $$…

The Bernstein operator $\mathbf{B}_n$ acts on a Schur function $S_\lambda$ by appending a part to the index, i.e., $\mathbf{B}_n S_\lambda=S_{(n,\lambda)}$. This provides a method of constructing the vertex operator representation of Schur…

Averaged operators have played an important role in fixed point theory in Hilbert spaces. They emerged as a necessity to obtain solutions to fixed point problems where the underlying operator is not contractive and thus renders Banach fixed…

The focus of this paper is on Ahlfors $Q$-regular compact sets $E\subset\mathbb{R}^n$ such that, for each $Q-2<\alpha\le 0$, the weighted measure $\mu_{\alpha}$ given by integrating the density $\omega(x)=\text{dist}(x, E)^\alpha$ yields a…

We study Chern-Simons theories at large $N$ with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines…

We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a mapping also respects matrix similarities, i.e., is a…

We introduce a modified version of the Whitney extension operators for collections of functions from a closed subset of $\mathbb{R}^n$ into scales of Banach spaces with smoothing operators. We prove an extension theorem for collections…

It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We…

The $\alpha$-Bernstein operators were initially introduced in the paper by Chen, X., Tan, J., Liu, Z., Xie, J. (2017) titled "Approximation of Functions by a New Family of Generalized Bernstein Operators" (Journal of Mathematical Analysis…

Let $N\ge 1$ and let $f\in C[0,\infty)$ be a nonnegative nondecreasing function and $u_0$ be a possibly singular nonnegative initial function. We are concerned with existence and nonexistence of a local in time nonnegative solution in a…

The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C}\rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell…

We prove the following generalisation of Schauder's fixed point conjecture: Let $C_1,...,C_n$ be convex subsets of a Hausdorff topological vector space. Suppose that the $C_i$ are closed in $C=C_1\cup...\cup C_n$. If $f:C\to C$ is a…