Related papers: Weighted approximation in $\mathbb{C}$

In this paper, we investigate the complex symmetric structure of generalized weighted composition operators $D_{m,\psi,\varphi}$ on the weighted Hardy space $H^2(\beta)$. We obtain explicit conditions for $ D_{m,\psi,\varphi}$ to be complex…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^N$. Given a continuous plurisubharmonic function $u$ on $\Omega$, we construct a sequence of Gaussian analytic functions $f_n$ on $\Omega$ associated with $u$ such that…

If $f$ is a real valued weakly lower semi-continous function on a Banach space $X$ and $C$ a weakly compact subset of $X$, we show that the set of $x \in X$ such that $z \mapsto \|x-z\|-f(z)$ attains its supremum on $C$ is dense in $X$. We…

Denote by $ B_X $ the unit ball of an infinite-dimensional complex Hilbert space $ X. $ Let $\psi \in H(B_X),$ the space of all holomorphic functions on the unit ball $B_X,$ $\varphi \in S(B_X)$ the set of holomorphic self-maps of $B_X. $…

It is shown that, assuming the Continuum Hypothesis, compact Hausdorff space of weight at most $\mathfrak{c}$ is a remainder in a soft compactification of $\mathbb{N}$. We also exhibit an example of a compact space of weight $\aleph_1$ --…

In certain classes of subharmonic functions u on C distinguished in terms of lower bounds for the Riesz measure of u, a sharp estimate is obtained for the rate of approximation by functions of the form log |f(z)|, where f is an entire…

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…

We prove that if $J$ is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors form a set of full Hausdorff dimension in $J$. The same is…

We prove that Ces\`{a}ro means of one-dimensional Walsh-Fourier series are uniformly bounded operators in the martingale Hardy space $H_{p}$ for $% 0<p<1/\left( 1+\alpha \right).$

In this paper we study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy…

It is shown that for every $\e\in (0,1)$, every compact metric space $(X,d)$ has a compact subset $S\subseteq X$ that embeds into an ultrametric space with distortion $O(1/\e)$, and $$\dim_H(S)\ge (1-\e)\dim_H(X),$$ where $\dim_H(\cdot)$…

We examine the surjectivity of isometries between weighted spaces of holomorphic functions. We show that for certain classical weights on the open unit disc all isometries of the weighted space of holomorphic functions, ${ \mathcal…

We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…

Let $E$ be an infinite-dimensional separable Hilbert space. We show that for every $C^1$ function $f:E\to\mathbb{R}^d$, every open set $U$ with $C_f:=\{x\in E:\,Df(x)\; \text{is not surjective}\}\subset U$ and every continuous function…

In this paper, we prove that into isometries and disjointness preserving linear maps from $C_0(X)$ into $C_0(Y)$ are essentially weighted composition operators $Tf = h\cdot f\circ\varphi$ for some continuous map $\varphi$ and some…

For $G$ an open set in $\mathbb{C}$ and $W$ a non-vanishing holomorphic function in $G$, in the late 1990's, Pritsker and Varga characterized pairs $(G,W)$ having the property that any $f$ holomorphic in $G$ can be locally uniformly…

Haver's near-selection theorem deals with approximate selections of Hausdorff continuous CE-valued mappings defined on $\sigma$-compact metrizable $C$-spaces. In the present paper, we extend this theorem to all paracompact $C$-spaces. The…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

Let $\mathcal{H}(b)$ denote the de Branges--Rovnyak space associated with a function $b$ in the unit ball of $H^\infty(\mathbb{C}_+)$. We study the boundary behavior of the derivatives of functions in $\mathcal{H}(b)$ and obtain weighted…

Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…