Matematychni Studii最新文献_第4页

On adequacy of full matrices 关于满矩阵的充分性

Matematychni Studii Pub Date : 2023-06-23 DOI: 10.30970/ms.59.2.115-122

A. Gatalevych, V. Shchedryk

引用次数: 0

Entire Bivariate Functions of Exponential Type II 指数型II的全二元函数

Matematychni Studii Pub Date : 2023-06-23 DOI: 10.30970/ms.59.2.156-167

Andriy Ivanovych Bandura, F. Nuray

引用次数: 2

Normality and uniqueness of homogeneous differential polynomials 齐次微分多项式的正规性和唯一性

Matematychni Studii Pub Date : 2023-06-23 DOI: 10.30970/ms.59.2.168-177

V. MatematychniStudii., No 59, R. S. Dyavanal, S. B. Kalakoti

引用次数: 0

Asymptotic solutions of singularly perturbed linear differential-algebraic equations with periodic coefficients 具有周期系数的奇摄动线性微分代数方程的渐近解

Matematychni Studii Pub Date : 2023-06-23 DOI: 10.30970/ms.59.2.187-200

S. Radchenko, V. Samoilenko, P. Samusenko

{"title":"Asymptotic solutions of singularly perturbed linear differential-algebraic equations with periodic coefficients","authors":"S. Radchenko, V. Samoilenko, P. Samusenko","doi":"10.30970/ms.59.2.187-200","DOIUrl":"https://doi.org/10.30970/ms.59.2.187-200","url":null,"abstract":"The paper deals with the problem of constructing asymptotic solutions for singular perturbed linear differential-algebraic equations with periodic coefficients. The case of multiple roots of a characteristic equation is studied. It is assumed that the limit pencil of matrices of the system has one eigenvalue of multiplicity n, which corresponds to two finite elementary divisors and two infinite elementary divisors whose multiplicity is greater than 1.A technique for finding the asymptotic solutions is developed and n formal linearly independent solutions are constructed for the corresponding differential-algebraic system. The developed algorithm for constructing formal solutions of the system is a nontrivial generalization of the corresponding algorithm for constructing asymptotic solutions of a singularly perturbed system of differential equations in normal form, which was used in the case of simple roots of the characteristic equation.The modification of the algorithm is based on the equalization method in a special way the coefficients at powers of a small parameter in algebraic systems of equations, from which the coefficients of the formal expansions of the searched solution are found. Asymptotic estimates for the terms of these expansions with respect to a small parameter are also given.For an inhomogeneous differential-algebraic system of equations with periodic coefficients, existence and uniqueness theorems for a periodic solution satisfying some asymptotic estimate are proved, and an algorithm for constructing the corresponding formal solutions of the system is developed. Both critical and non-critical cases are considered.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42707806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On entire Dirichlet series similar to Hadamard compositions 关于类似于Hadamard合成的整个Dirichlet级数

Matematychni Studii Pub Date : 2023-06-23 DOI: 10.30970/ms.59.2.132-140

O. Mulyava, M. Sheremeta

{"title":"On entire Dirichlet series similar to Hadamard compositions","authors":"O. Mulyava, M. Sheremeta","doi":"10.30970/ms.59.2.132-140","DOIUrl":"https://doi.org/10.30970/ms.59.2.132-140","url":null,"abstract":"A function $F(s)=sum_{n=1}^{infty}a_nexp{slambda_n}$ with $0lelambda_nuparrow+infty$ is called the Hadamard composition of the genus $mge 1$ of functions $F_j(s)=sum_{n=1}^{infty}a_{n,j}exp{slambda_n}$ if $a_n=P(a_{n,1},...,a_{n,p})$, where$P(x_1,...,x_p)=sumlimits_{k_1+dots+k_p=m}c_{k_1...k_p}x_1^{k_1}cdot...cdot x_p^{k_p}$ is a homogeneous polynomial of degree $mge 1$. Let $M(sigma,F)=sup{|F(sigma+it)|:,tin{Bbb R}}$ and functions $alpha,,beta$ be positive continuous and increasing to $+infty$ on $[x_0, +infty)$. To characterize the growth of the function $M(sigma,F)$, we use generalized order $varrho_{alpha,beta}[F]=varlimsuplimits_{sigmato+infty}dfrac{alpha(ln,M(sigma,F))}{beta(sigma)}$, generalized type$T_{alpha,beta}[F]=varlimsuplimits_{sigmato+infty}dfrac{ln,M(sigma,F)}{alpha^{-1}(varrho_{alpha,beta}[F]beta(sigma))}$and membership in the convergence class defined by the condition$displaystyle int_{sigma_0}^{infty}frac{ln,M(sigma,F)}{sigmaalpha^{-1}(varrho_{alpha,beta}[F]beta(sigma))}dsigma<+infty.$Assuming the functions $alpha, beta$ and $alpha^{-1}(cbeta(ln,x))$ are slowly increasing for each $cin (0,+infty)$ and $ln,n=O(lambda_n)$ as $nto infty$, it is proved, for example, that if the functions $F_j$ have the same generalized order $varrho_{alpha,beta}[F_j]=varrhoin (0,+infty)$ and the types $T_{alpha,beta}[F_j]=T_jin [0,+infty)$, $c_{m0...0}=cnot=0$, $|a_{n,1}|>0$ and $|a_{n,j}|= o(|a_{n,1}|)$ as $ntoinfty$ for $2le jle p$, and $F$ is the Hadamard composition of genus$mge 1$ of the functions $F_j$ then $varrho_{alpha,beta}[F]=varrho$ and $displaystyle T_{alpha,beta}[F]le sum_{k_1+dots+k_p=m}(k_1T_1+...+k_pT_p).$It is proved also that $F$ belongs to the generalized convergence class if and only ifall functions $F_j$ belong to the same convergence class.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44846177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximation of classes of Poisson integrals by Fejer means 一类Poisson积分的Fejer平均逼近

Matematychni Studii Pub Date : 2023-05-16 DOI: 10.30970/ms.59.2.201-204

O. Rovenska

{"title":"Approximation of classes of Poisson integrals by Fejer means","authors":"O. Rovenska","doi":"10.30970/ms.59.2.201-204","DOIUrl":"https://doi.org/10.30970/ms.59.2.201-204","url":null,"abstract":"The paper is devoted to the investigation of problem of approximation of continuous periodic functions by trigonometric polynomials, which are generated by linear methods of summation of Fourier series. \u0000The simplest example of a linear approximation of periodic functions is the approximation of functions by partial sums of their Fourier series. However, the sequences of partial Fourier sums are not uniformly convergent over the class of continuous periodic functions. Therefore, many studies devoted to the research of the approximative properties of approximation methods, which are generated by transformations of the partial sums of Fourier series and allow us to construct sequences of trigonometrical polynomials that would be uniformly convergent for the whole class of continuous functions. Particularly, Fejer sums have been widely studied recently. One of the important problems in this area is the study of asymptotic behavior of the sharp upper bounds over a given class of functions of deviations of the trigonometric polynomials. \u0000In the paper, we study upper asymptotic estimates for deviations between a function and the Fejer means for the Fourier series of the function. The asymptotic behavior is considered for the functions represented by the Poisson integrals of periodic functions of a real variable. The mentioned classes consist of analytic functions of a real variable. These functions can be regularly extended into the corresponding strip of the complex plane.An asymptotic equality for the upper bounds of Fejer means deviations on classes of Poisson integrals was obtained.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45728919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Metric characterizations of some subsets of the real line 实直线若干子集的度量特征

Matematychni Studii Pub Date : 2023-05-13 DOI: 10.30970/ms.59.2.205-214

I. Banakh, T. Banakh, Maria Kolinko, A. Ravsky

{"title":"Metric characterizations of some subsets of the real line","authors":"I. Banakh, T. Banakh, Maria Kolinko, A. Ravsky","doi":"10.30970/ms.59.2.205-214","DOIUrl":"https://doi.org/10.30970/ms.59.2.205-214","url":null,"abstract":"A metric space $(X,mathsf{d})$ is called a {em subline} if every 3-element subset $T$ of $X$ can be written as $T={x,y,z}$ for some points $x,y,z$ such that $mathsf{d}(x,z)=mathsf{d}(x,y)+mathsf{d}(y,z)$. By a classical result of Menger, every subline of cardinality $ne 4$ is isometric to a subspace of the real line. A subline $(X,mathsf{d})$ is called an {em $n$-subline} for a natural number $n$ if for every $cin X$ and positive real number $rinmathsf{d}[X^2]$, the sphere ${mathsf S}(c;r):={xin Xcolon mathsf{d}(x,c)=r}$ contains at least $n$ points. We prove that every $2$-subline is isometric to some additive subgroup of the real line. Moreover, for every subgroup $Gsubseteq{mathbb R}$, a metric space $(X,mathsf{d})$ is isometric to $G$ if and only if $X$ is a $2$-subline with $mathsf{d}[X^2]=G_+:= Gcap[0,infty)$. A metric space $(X,mathsf{d})$ is called a {em ray} if $X$ is a $1$-subline and $X$ contains a point $oin X$ such that for every $rinmathsf{d}[X^2]$ the sphere ${mathsf S}(o;r)$ is a singleton. We prove that for a subgroup $Gsubseteq{mathbb Q}$, a metric space $(X,mathsf{d})$ is isometric to the ray $G_+$ if and only if $X$ is a ray with $mathsf{d}[X^2]=G_+$. A metric space $X$ is isometric to the ray ${mathbb R}_+$ if and only if $X$ is a complete ray such that ${mathbb Q}_+subseteq mathsf{d}[X^2]$. On the other hand, the real line contains a dense ray $Xsubseteq{mathbb R}$ such that $mathsf{d}[X^2]={mathbb R}_+$.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47173806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Global estimates for sums of absolutely convergent Dirichlet series in a half-plane 半平面上绝对收敛Dirichlet级数和的全局估计

Matematychni Studii Pub Date : 2023-03-29 DOI: 10.30970/ms.59.1.60-67

P. Filevych, O. B. Hrybel

{"title":"Global estimates for sums of absolutely convergent Dirichlet series in a half-plane","authors":"P. Filevych, O. B. Hrybel","doi":"10.30970/ms.59.1.60-67","DOIUrl":"https://doi.org/10.30970/ms.59.1.60-67","url":null,"abstract":"Let $(lambda_n)_{n=0}^{+infty}$ be a nonnegative sequence increasing to $+infty$, $F(s)=sum_{n=0}^{+infty} a_ne^{slambda_n}$ be an absolutely convergent Dirichlet series in the half-plane ${sinmathbb{C}colon operatorname{Re} s<0}$, and let, for every $sigma<0$, $mathfrak{M}(sigma,F)=sum_{n=0}^{+infty} |a_n|e^{sigmalambda_n}$. \u0000Suppose that $Phicolon (-infty,0)tooverline{mathbb{R}}$ is a function, and let $widetilde{Phi}(x)$ be the Young-conjugate function of $Phi(sigma)$, i.e.$widetilde{Phi}(x)=sup{xsigma-alpha(sigma)colon sigma<0}$ for all $xinmathbb{R}$. In the article, the following two statements are proved: \u0000(i) There exist constants $thetain(0,1)$ and $Cinmathbb{R}$ such that$lnmathfrak{M}(sigma,F)lePhi(thetasigma)+C$ for all $sigma<0$ if and only if there exist constants $deltain(0, 1)$ and $cinmathbb{R}$ such that $lnsum_{m=0}^n|a_m|le-widetilde{Phi}(lambda_n/delta)+c$ for all integers $nge0$ (Theorem 2); \u0000(ii) For every $thetain(0,1)$ there exists a real constant $C=C(delta)$ such that $lnmathfrak{M}(sigma,F)lePhi( thetasigma)+C$ for all $sigma<0$ if and only if for every $deltain(0,1)$ there exists a real constant $c=c(delta)$ such that $lnsum_{m=0}^n|a_m|le-widetilde{Phi}(lambda_n/delta)+c$ for all integers $nge0$ (Theorem 3).iii) Let $Phi$ be a continuous positive increasing function on $mathbb{R}$ such that $Phi(sigma)/sigmato+infty$, $sigmato+ infty$ and $F$ be a entire Dirichlet series. \u0000For every $q>1$ there exists a constant $C=C(q)inmathbb{R}$ such that $lnmathfrak{M}(sigma,F)le Phi(qsigma)+C,quad sigmainmathbb{R},$ holds if and only if for every $delta in(0,1)$ there exist constants $c=c(delta)inmathbb{R}$ and $n_0=n_0(delta)inmathbb{N}_0$ such that $ln sum_{m=n}^{+infty}|a_m|le-widetilde{Phi}(deltalambda_n)+c,quad nge n_0$ Theorem 5. \u0000These results are analogous to some results previously obtained by M.M. Sheremeta for entire Dirichlet series.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46052251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Binormal and complex symmetric weighted composition operators on the Fock Space over $mathbb{C}$ $mathbb｛C｝上Fock空间上的二重和复对称加权复合算子$

Matematychni Studii Pub Date : 2023-03-28 DOI: 10.30970/ms.59.1.106-112

C. Santhoshkumar

引用次数: 0

Spaces of series in system of functions 函数系统中的级数空间

Matematychni Studii Pub Date : 2023-03-28 DOI: 10.30970/ms.59.1.46-59

M. Sheremeta

引用次数: 0