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Convergence of the Fourier Series in Meixner–Sobolev Polynomials and Approximation Properties of Its Partial Sums Meixner-Sobolev 多项式中傅里叶级数的收敛性及其部分和的逼近特性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030027
R. M. Gadzhimirzaev
{"title":"Convergence of the Fourier Series in Meixner–Sobolev Polynomials and Approximation Properties of Its Partial Sums","authors":"R. M. Gadzhimirzaev","doi":"10.1134/s0001434624030027","DOIUrl":"https://doi.org/10.1134/s0001434624030027","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the convergence of Fourier series in the polynomial system <span>({m_{n,N}^{alpha,r}(x)})</span> orthonormal in the sense of Sobolev and generated by the system of modified Meixner polynomials. In particular, we show that the Fourier series of <span>(fin W^r_{l^p_{rho_N}(Omega_delta)})</span> in this system converges to <span>(f)</span> pointwise on the grid <span>(Omega_delta)</span> as <span>(pge2)</span>. In addition, we study the approximation properties of partial sums of Fourier series in the system <span>({m_{n,N}^{0,r}(x)})</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trigonometric Polynomials with Frequencies in the Set of Cubes 具有立方集合中频率的三角多项式
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030052
M. R. Gabdullin, S. V. Konyagin
{"title":"Trigonometric Polynomials with Frequencies in the Set of Cubes","authors":"M. R. Gabdullin, S. V. Konyagin","doi":"10.1134/s0001434624030052","DOIUrl":"https://doi.org/10.1134/s0001434624030052","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We prove that for any <span>(varepsilon&gt;0)</span> and any trigonometric polynomial <span>(f)</span> with frequencies in the set <span>({n^3: N leq nleq N+N^{2/3-varepsilon}})</span> one has </p><span>$$|f|_4 ll varepsilon^{-1/4}|f|_2$$</span><p> with implied constant being absolute. We also show that the set <span>({n^3: Nleq nleq N+(0.5N)^{1/2}})</span> is a Sidon set. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Angles between Linear Subspaces in $$mathbb R^4$$ and the Singularity 论$$mathbb R^4$$中线性子空间与奇点之间的角度
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030131
A. O. Chebotarenko
{"title":"On Angles between Linear Subspaces in $$mathbb R^4$$ and the Singularity","authors":"A. O. Chebotarenko","doi":"10.1134/s0001434624030131","DOIUrl":"https://doi.org/10.1134/s0001434624030131","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We generalize the Khinchin singularity phenomenon for the problem in which, for a given irrational linear subspace, rational subspaces forming the least angle with the given subspace are sought. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Boundedness of the Fractional Maximal Operator, the Riesz Potential, and Their Commutators in Orlicz Spaces 论奥利兹空间中分数最大算子、里兹势及其换元的有界性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030180
A. R. Aliev, R. A. Aliev
{"title":"On the Boundedness of the Fractional Maximal Operator, the Riesz Potential, and Their Commutators in Orlicz Spaces","authors":"A. R. Aliev, R. A. Aliev","doi":"10.1134/s0001434624030180","DOIUrl":"https://doi.org/10.1134/s0001434624030180","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, conditions are found for the boundedness of the fractional maximal operator, the Riesz potential, and their commutators in Orlicz spaces. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Locally Chebyshev Sets 论局部切比雪夫集
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030362
K. S. Shklyaev
{"title":"On Locally Chebyshev Sets","authors":"K. S. Shklyaev","doi":"10.1134/s0001434624030362","DOIUrl":"https://doi.org/10.1134/s0001434624030362","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> It is proved that every connected boundedly compact locally Chebyshev set in a normed space is a Chebyshev set. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$$n$$ -Dimensional Generalizations of a Thébault Conjecture 泰博猜想的$n$$维广义化
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030337
Q. H. Tran, B. Herrera
{"title":"$$n$$ -Dimensional Generalizations of a Thébault Conjecture","authors":"Q. H. Tran, B. Herrera","doi":"10.1134/s0001434624030337","DOIUrl":"https://doi.org/10.1134/s0001434624030337","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> This paper presents some generalizations of a Thébault conjecture, provides an analog of the Thébault conjecture for the <span>(n)</span>-simplex, and also solves a conjecture in a 2022 paper by the authors by using linear algebra. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation by Refinement Masks 用细化掩模进行逼近
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030076
E. A. Lebedeva
{"title":"Approximation by Refinement Masks","authors":"E. A. Lebedeva","doi":"10.1134/s0001434624030076","DOIUrl":"https://doi.org/10.1134/s0001434624030076","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We construct a Parseval wavelet frame with compact support for an arbitrary continuous <span>(2pi)</span>-periodic function <span>(f)</span>, <span>(f(0)=1)</span>, satisfying the inequality <span>(|f(x)|^2+|f(x+pi)|^2le 1)</span>. The frame refinement mask uniformly approximates <span>(f)</span>. The refining function has stable integer shifts. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Common Fixed Point Theorems for Contractive Mappings of Integral Type in $$b$$ -Metric Spaces $$b$$ -度量空间中积分型收缩映射的共用定点定理
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030258
Hongyan Guan, Jinze Gou
{"title":"Common Fixed Point Theorems for Contractive Mappings of Integral Type in $$b$$ -Metric Spaces","authors":"Hongyan Guan, Jinze Gou","doi":"10.1134/s0001434624030258","DOIUrl":"https://doi.org/10.1134/s0001434624030258","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> This paper is the first to introduce a fixed point problem of integral type in a <span>(b)</span>-metric space. We study sufficient conditions for the existence and uniqueness of a common fixed point of contractive mappings of integral type. We also give two examples to support our results. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
S. R. Nasyrov’s Problem of Approximation by Simple Partial Fractions on an Interval S.S. R. 纳西洛夫的区间简单部分分数逼近问题
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030234
P. A. Borodin, A. M. Ershov
{"title":"S. R. Nasyrov’s Problem of Approximation by Simple Partial Fractions on an Interval","authors":"P. A. Borodin, A. M. Ershov","doi":"10.1134/s0001434624030234","DOIUrl":"https://doi.org/10.1134/s0001434624030234","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In 2014, S. R. Nasyrov asked whether it is true that simple partial fractions (logarithmic derivatives of complex polynomials) with poles on the unit circle are dense in the complex space <span>(L_2[-1,1])</span>. In 2019, M. A. Komarov answered this question in the negative. The present paper contains a simple solution of Nasyrov’s problem different from Komarov’s one. Results related to the following generalizing questions are obtained: (a) of the density of simple partial fractions with poles on the unit circle in weighted Lebesgue spaces on <span>([-1,1])</span>; (b) of the density in <span>(L_2[-1,1])</span> of simple partial fractions with poles on the boundary of a given domain for which <span>([-1,1])</span> is an inner chord. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation Numbers of the Two-Dimensional Rectangular Hardy Operator 二维矩形哈代算子的近似数
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030118
V. D. Stepanov, E. P. Ushakova
{"title":"Approximation Numbers of the Two-Dimensional Rectangular Hardy Operator","authors":"V. D. Stepanov, E. P. Ushakova","doi":"10.1134/s0001434624030118","DOIUrl":"https://doi.org/10.1134/s0001434624030118","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Upper and lower bounds are obtained for the approximation numbers of the two-dimensional rectangular Hardy operator on weighted Lebesgue spaces on <span>(mathbb{R}_+^2)</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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