arXiv subjects

Sofiya Ostrovska

Publications and source records attributed to Sofiya Ostrovska.

At least 19 recordsLinked to original sources

arXiv2024

The impact of the limit $q$-Durrmeyer operator on continuous functions

The limit $q$-Durrmeyer operator, $D_{\infty,q},$ was introduced and its approximation properties were investigated by V. Gupta in 2008 during a study of $q$-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of $D_{\infty,q}$. The interrelation between the analytic properties of a function $f$ and the rate of growth for $D_{\infty,q}f$ are established, and the sharpness of the obtained results are demonstrated.

math.CV↗

arXiv2023

Dvoretzky-type theorem for locally finite subsets of a Hilbert space

The main result of the paper: Given any $\varepsilon>0$, every locally finite subset of $\ell_2$ admits a $(1+\varepsilon)$-bilipschitz embedding into an arbitrary infinite-dimensional Banach space. The result is based on two results which are of independent interest: (1) A direct sum of two finite-dimensional Euclidean spaces contains a sub-sum of a controlled dimension which is $\varepsilon$-close to a direct sum with respect to a $1$-unconditional basis in a two-dimensional space. (2) For any finite-dimensional Banach space $Y$ and its direct sum $X$ with itself with respect to a $1$-unconditional basis in a two-dimensional space, there exists a $(1+\varepsilon)$-bilipschitz embedding of $Y$ into $X$ which on a small ball coincides with the identity map onto the first summand and on a complement of a large ball coincides with the identity map onto the second summand.

math.FA↗

arXiv2022

Complementability of isometric copies of $\ell_1$ in transportation cost spaces

This work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as Arens-Eells spaces, Lipschitz-free spaces, and Wasserstein spaces. The main outcome of this paper states that if a metric space $X$ is such that the transportation cost space on $X$ contains an isometric copy of $\ell_1$, then it contains a $1$-complemented isometric copy of $\ell_1$.

math.FA↗

arXiv2021

Isometric structure of transportation cost spaces on finite metric spaces

The paper is devoted to isometric Banach-space-theoretical structure of transportation cost (TC) spaces on finite metric spaces. The TC spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein spaces. A new notion of a roadmap pertinent to a transportation problem on a finite metric space has been introduced and used to simplify proofs for the results on representation of TC spaces as quotients of $\ell_1$ spaces on the edge set over the cycle space. A Tolstoi-type theorem for roadmaps is proved, and directed subgraphs of the canonical graphs, which are supports of maximal optimal roadmaps, are characterized. Possible obstacles for a TC space on a finite metric space $X$ preventing them from containing subspaces isometric to $\ell_\infty^n$ have been found in terms of the canonical graph of $X$. The fact that TC spaces on diamond graphs do not contain $\ell_\infty^4$ isometrically has been derived. In addition, a short overview of known results on the isometric structure of TC spaces on finite metric spaces is presented.

math.FA↗

arXiv2020

On relations between transportation cost spaces and $\ell_1$

The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient condition on an infinite metric space $M$, under which the transportation cost space on $M$ contains an isometric copy of $\ell_1$. The obtained condition is applied to answer the open questions asked by Cúth and Johanis (2017) concerning several specific metric spaces. (2) The description of the transportation cost space of a weighted finite graph $G$ as the quotient $\ell_1(E(G))/Z(G)$, where $E(G)$ is the edge set and $Z(G)$ is the cycle space of $G$. This is a generalization of the previously known result to the case of any finite metric space.

math.FA↗

arXiv2019

On the q-moment determinacy of probability distributions

Given $0<q<1,$ every absolutely continuous distribution can be described in two different ways: in terms of a probability density function and also in terms of a $q$-density. Correspondingly, it has a sequence of moments and a sequence of $q$-moments if those exist. In this article, new conditions on the $q$-moment determinacy of probability distributions are derived. In addition, results related to the comparison of the properties of probability distributions with respect to the moment and $q$-moment determinacy are presented.

math.PR↗

arXiv2019

Discrete Stieltjes classes for log-Heine type distributions

The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be easy to indicate another distribution with the same moments. Mostly, the Stieltjes classes have been considered for absolutely continuous distributions. In this work, a new approach for constructing them in the discrete case is presented. Examples for some widely used discrete distributions are provided.

math.PR↗

arXiv2019

Power Lindley distribution and software metrics

The Lindley distribution and its numerous generalizations are widely used in statistical and engineering practice. Recently, a power transformation of Lindley distribution, called the power Lindley distribution, has been introduced by M. E. Ghitany et al., who initiated the investigation of its properties and possible applications. In this article, new results on the power Lindley distribution are presented. The focus of this work is on the moment-(in)determinacy of the distribution for various values of the parameters. Afterwards, certain applications are provided to describe data sets of software metrics.

math.ST↗

arXiv2019

q-Stieltjes classes for some families of q-distributions

The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly an infinite family of probability densities with the same sequence of moments. In this paper, the notion of $q$-moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either $q$-moment determinate or indeterminate in terms of its $q$-density have been obtained. Also, a $q$-analogue of Stieltjes classes is defined for $q$-distributions and $q$-Stieltjes classes have been constructed for a family of $q$-densities of $q$-moment indeterminate distributions.

math.PR↗

arXiv2019

Generalized transportation cost spaces

The paper is devoted to the geometry of transportation cost spaces and their generalizations introduced by Melleray, Petrov, and Vershik (2008). Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein $1$ spaces. In this work, the existence of metric spaces with the following properties is proved: (1) uniformly discrete infinite metric spaces transportation cost spaces on which do not contain isometric copies of $\ell_1$, this result answers a question raised by Cuth and Johanis (2017); (2) locally finite metric spaces which admit isometric embeddings only into Banach spaces containing isometric copies of $\ell_1$; (3) metric spaces for which the double-point norm is not a norm. In addition, it is proved that the double-point norm spaces corresponding to trees are close to $\ell_\infty^d$ of the corresponding dimension, and that for all finite metric spaces $M$, except a very special class, the infimum of all seminorms for which the embedding of $M$ into the corresponding seminormed space is isometric, is not a seminorm.

math.FA↗

arXiv2018

Uncorrelatedness sets of discrete uniform distributions via Vandermonde-type determinants

Given random variables $X$ and $Y$ having finite moments of all orders, their uncorrelatedness set is defined as the set of all pairs $(j,k)\in{\mathbb N}^2,$ for which $X^j$ and $Y^k$ are uncorrelated. It is known that, broadly put, any subset of ${\mathbb N}^2$ can serve as an uncorrelatedness set. This claim ceases to be true for random variables with prescribed distributions, in which case the need arises so as to identify the admissible uncorrelatedness sets. This paper studies the uncorrelatedness sets for positive random variables uniformly distributed on three points. Some general features of these sets are derived. Two related Vandermonde-type determinants are examined and applied to describe uncorrelatedness sets in specific cases.

math.PR↗

arXiv2018

On Lin's condition for products of random variables with joint singular distribution

Lin's condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin's condition for functions of random variables have emerged. In this work, Lin's condition is studied for the product of random variables with given densities in the case when their joint distribution is singular.

math.PR↗

arXiv2018

The distance between two limit $q$-Bernstein operators

For $q\in(0,1),$ let $B_q$ denote the limit $q$-Bernstein operator. In this paper, the distance between $B_q$ and $B_r$ for distinct $q$ and $r$ in the operator norm on $C[0,1]$ is estimated, and it is proved that $1\leqslant \|B_q-B_r\|\leqslant 2,$ where both of the equalities can be attained. To elaborate more, the distance depends on whether or not $r$ and $q$ are rational powers of each other. For example, if $r^j\neq q^m$ for all $j,m\in \mathbb{N},$ then $\|B_q-B_r\|=2,$ and if $r=q^m, m\in \mathbb{N},$ then $\|B_q-B_r\|=2(m-1)/m.$

math.FA↗

arXiv2017

On embeddings of locally finite metric spaces into $\ell_p$

It is known that if finite subsets of a locally finite metric space $M$ admit $C$-bilipschitz embeddings into $\ell_p$ $(1\le p\le \infty)$, then for every $ε>0$, the space $M$ admits a $(C+ε)$-bilipschitz embedding into $\ell_p$. The goal of this paper is to show that for $p\ne 2,\infty$ this result is sharp in the sense that $ε$ cannot be dropped out of its statement.

math.FA↗

arXiv2017

Distortion in the finite determination result for embeddings of locally finite metric spaces into Banach spaces

Given a Banach space $X$ and a real number $α\ge 1$, we write: (1) $D(X)\leα$ if, for any locally finite metric space $A$, all finite subsets of which admit bilipschitz embeddings into $X$ with distortions $\le C$, the space $A$ itself admits a bilipschitz embedding into $X$ with distortion $\le α\cdot C$; (2) $D(X)=α^+$ if, for every $\varepsilon>0$, the condition $D(X)\leα+\varepsilon$ holds, while $D(X)\leα$ does not; (3) $D(X)\le α^+$ if $D(X)=α^+$ or $D(X)\le α$. It is known that $D(X)$ is bounded by a universal constant, but the available estimates for this constant are rather large. The following results have been proved in this work: (1) $D((\oplus_{n=1}^\infty X_n)_p)\le 1^+$ for every nested family of finite-dimensional Banach spaces $\{X_n\}_{n=1}^\infty$ and every $1\le p\le \infty$. (2) $D((\oplus_{n=1}^\infty \ell^\infty_n)_p)=1^+$ for $1<p<\infty$. (3) $D(X)\le 4^+$ for every Banach space $X$ with no nontrivial cotype. Statement (3) is a strengthening of the Baudier-Lancien result (2008).

math.FA↗

arXiv2017

On Lin's condition for products of random variables

The paper presents an elaboration of some results on Lin's conditions. A new proof of the fact that if densities of independent random variables $ξ_1$ and $ξ_2$ satisfy Lin's condition, the same is true for their product is presented. Also, it is shown that without the condition of independence, the statement is no longer valid.

math.PR↗

arXiv2017

Distortion of embeddings of binary trees into diamond graphs

Diamond graphs and binary trees are important examples in the theory of metric embeddings and also in the theory of metric characterizations of Banach spaces. Some results for these families of graphs are parallel to each other, for example superreflexivity of Banach spaces can be characterized both in terms of binary trees (Bourgain, 1986) and diamond graphs (Johnson-Schechtman, 2009). In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. This question was answered in the negative by Ostrovskii (2014), who left it open to determine the order of growth of the distortions. The main purpose of this paper is to get a sharp-up-to-a-logarithmic-factor estimate for the distortions of embeddings of binary trees into diamond graphs, and, more generally, into diamond graphs of any finite branching $k\ge 2$. Estimates for distortions of embeddings of diamonds into infinitely branching diamonds are also obtained.

math.MG↗

arXiv2015

Induced scattering limits on fast radio bursts from stellar coronae

The origin of fast radio bursts remains a puzzle. Suggestions have been made that they are produced within the Earth atmosphere, in stellar coronae, in other galaxies or at cosmological distances. If they are extraterrestrial, the implied brightness temperature is very high, and therefore, the induced scattering places constraints on possible models. In this paper, constraints are obtained on flares from coronae of nearby stars. It is shown that the radio pulses with the observed power could not be generated if the plasma density within and in the nearest vicinity of the source is as high as it is necessary in order to provide the observed dispersion measure. However, one cannot exclude a possibility that the pulses are generated within a bubble with a very low density and pass through the dense plasma only in the outer corona.

astro-ph.HE↗