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Kolmogorov Equations for Degenerate Ornstein–Uhlenbeck Operators 退化奥恩斯坦-乌伦贝克算子的柯尔莫哥洛夫方程
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010038
V. I. Bogachev, S. V. Shaposhnikov
{"title":"Kolmogorov Equations for Degenerate Ornstein–Uhlenbeck Operators","authors":"V. I. Bogachev, S. V. Shaposhnikov","doi":"10.1134/s0037446624010038","DOIUrl":"https://doi.org/10.1134/s0037446624010038","url":null,"abstract":"<p>We consider Kolmogorov operators with constant diffusion matrices and linear drifts, i.e.,\u0000Ornstein–Uhlenbeck operators, and show that\u0000all solutions to the corresponding stationary Fokker–Planck–Kolmogorov equations (including signed solutions)\u0000are invariant measures for the generated semigroups. This also gives a relatively explicit description of all solutions.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"30 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769987","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 Approximative Properties of Fourier Series in Laguerre–Sobolev Polynomials 论拉盖尔-索博列夫多项式中傅里叶级数的近似性质
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s003744662401004x
R. M. Gadzhimirzaev
{"title":"On the Approximative Properties of Fourier Series in Laguerre–Sobolev Polynomials","authors":"R. M. Gadzhimirzaev","doi":"10.1134/s003744662401004x","DOIUrl":"https://doi.org/10.1134/s003744662401004x","url":null,"abstract":"<p>Considering the approximation of a function <span>( f )</span> from a Sobolev space\u0000by the partial sums of Fourier series in a system of Sobolev orthogonal polynomials\u0000generated by classical Laguerre polynomials,\u0000we obtain an estimate for the convergence rate of the partial sums to <span>( f )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"6 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769752","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
Admissible Inference Rules of Modal WCP-Logics 模态 WCP 逻辑的可容许推理规则
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010142
V. V. Rimatskiy
{"title":"Admissible Inference Rules of Modal WCP-Logics","authors":"V. V. Rimatskiy","doi":"10.1134/s0037446624010142","DOIUrl":"https://doi.org/10.1134/s0037446624010142","url":null,"abstract":"<p>We study admissible rules\u0000for the extensions of the modal logics S4\u0000and GL\u0000with the weak co-covering property\u0000and describe some explicit independent basis for the admissible rules of these logics.\u0000The resulting basis consists of an infinite sequence of rules\u0000in compact and simple form.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"17 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769845","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
Hilbert–Pólya Operators in Krein Spaces 克雷因空间中的希尔伯特-波利亚算子
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010087
V. V. Kapustin
{"title":"Hilbert–Pólya Operators in Krein Spaces","authors":"V. V. Kapustin","doi":"10.1134/s0037446624010087","DOIUrl":"https://doi.org/10.1134/s0037446624010087","url":null,"abstract":"<p>We construct some class of selfadjoint operators in the Krein spaces consisting of functions on\u0000the straight line <span>( {operatorname{Re}s=frac{1}{2}} )</span>.\u0000Each of these operators is a rank-one perturbation of a selfadjoint operator\u0000in the corresponding Hilbert space\u0000and has eigenvalues complex numbers of the form <span>( frac{1}{s(1-s)} )</span>,\u0000where <span>( s )</span> ranges over the set of nontrivial zeros of the Riemann zeta-function.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"35 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769753","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
Oriented Rotatability Exponents of Solutions to Homogeneous Autonomous Linear Differential Systems 同构自洽线性微分系统解的定向可旋转性指数
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s003744662401018x
A. Kh. Stash
{"title":"Oriented Rotatability Exponents of Solutions to Homogeneous Autonomous Linear Differential Systems","authors":"A. Kh. Stash","doi":"10.1134/s003744662401018x","DOIUrl":"https://doi.org/10.1134/s003744662401018x","url":null,"abstract":"<p>We fully study the oriented rotatability exponents of solutions to\u0000homogeneous autonomous linear differential systems and\u0000establish that the strong and weak oriented\u0000rotatability exponents coincide for each solution to an autonomous system\u0000of differential equations. We also show that the\u0000spectrum of this exponent (i.e., the set of values of nonzero\u0000solutions) is naturally determined by the number-theoretic\u0000properties of the set of imaginary parts of the eigenvalues of the\u0000matrix of a system. This set (in contrast to the oscillation\u0000and wandering exponents) can contain other than zero values and the\u0000imaginary parts of the eigenvalues of the system matrix; moreover,\u0000the power of this spectrum can be exponentially large in\u0000comparison with the dimension of the space.\u0000In demonstration we use the basics of ergodic theory,\u0000in particular, Weyl’s Theorem.\u0000We prove that the spectra of all oriented rotatability exponents\u0000of autonomous systems with a symmetrical\u0000matrix consist of a single zero value.\u0000We also establish relationships\u0000between the main values of the exponents on a set of autonomous systems.\u0000The obtained results allow us to conclude that the exponents of\u0000oriented rotatability, despite their simple and natural definitions,\u0000are not analogs of the Lyapunov exponent in oscillation theory.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"17 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769746","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
Birman–Hilden Bundles. I 比尔曼-希尔登捆包I
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010117
A. V. Malyutin
{"title":"Birman–Hilden Bundles. I","authors":"A. V. Malyutin","doi":"10.1134/s0037446624010117","DOIUrl":"https://doi.org/10.1134/s0037446624010117","url":null,"abstract":"<p>A topological fibered space is a Birman–Hilden space\u0000whenever in each isotopic pair of its fiber-preserving\u0000(taking each fiber to a fiber) self-homeomorphisms\u0000the homeomorphisms are also fiber-isotopic\u0000(isotopic through fiber-preserving homeomorphisms).\u0000We present a series of sufficient conditions\u0000for a fiber bundle over the circle\u0000to be a Birman–Hilden space.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"62 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769805","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
A Spectral Criterion for Power-Law Convergence Rate in the Ergodic Theorem for  $ {��}^{d} $ and  $ {��}^{d} $ Actions {��}^{d}和{��}^{d}的幂律收敛率谱标准
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010099
A. G. Kachurovskii, I. V. Podvigin, V. È. Todikov, A. Zh. Khakimbaev
{"title":"A Spectral Criterion for Power-Law Convergence Rate in the Ergodic Theorem for  $ {��}^{d} $ and  $ {��}^{d} $ Actions","authors":"A. G. Kachurovskii, I. V. Podvigin, V. È. Todikov, A. Zh. Khakimbaev","doi":"10.1134/s0037446624010099","DOIUrl":"https://doi.org/10.1134/s0037446624010099","url":null,"abstract":"<p>We prove the equivalence of the power-law convergence rate in the <span>( L_{2} )</span>-norm\u0000of ergodic averages for <span>( {𝕑}^{d} )</span> and <span>( {𝕉}^{d} )</span> actions and the same\u0000power-law estimate for the spectral measure of symmetric <span>( d )</span>-dimensional\u0000parallelepipeds: for the degrees that are roots of some special symmetric\u0000polynomial in <span>( d )</span> variables. Particularly, all possible range\u0000of power-law rates is covered for <span>( d=1 )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"35 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769745","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
Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5 具有阶数为 5 的烈-无势同一性的各种替代代数的结构
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010130
S. V. Pchelintsev
{"title":"Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5","authors":"S. V. Pchelintsev","doi":"10.1134/s0037446624010130","DOIUrl":"https://doi.org/10.1134/s0037446624010130","url":null,"abstract":"<p>We construct an additive basis for a relatively free\u0000alternative algebra of Lie-nilpotent degree 5,\u0000describe the associative center and core of this algebra, and find\u0000the T-generators of the full center.\u0000Also, we give some asymptotic estimate for the codimension\u0000of the T-ideal generated by a commutator of degree 5\u0000in a free alternative algebra, and find\u0000a finite-dimensional superalgebra that\u0000generates the variety of alternative algebras\u0000with the Lie-nilpotency of the selfadjoint operator of degree 5.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769623","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
The Riesz–Zygmund Sums of Fourier–Chebyshev Rational Integral Operators and Their Approximation Properties 傅里叶-切比雪夫有理积分算子的里兹-齐格蒙德和及其近似性质
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-01-01 DOI: 10.1134/s0037446624010129
{"title":"The Riesz–Zygmund Sums of Fourier–Chebyshev Rational Integral Operators and Their Approximation Properties","authors":"","doi":"10.1134/s0037446624010129","DOIUrl":"https://doi.org/10.1134/s0037446624010129","url":null,"abstract":"<h3>Abstract</h3> <p>Studying the approximation properties of a certain Riesz–Zygmund sum of Fourier–Chebyshev rational integral operators with constraints on the number of geometrically distinct poles, we obtain an integral expression of the operators. We find upper bounds for pointwise and uniform approximations to the function <span> <span>( |x|^{s} )</span> </span> with <span> <span>( sin(0,2) )</span> </span> on the segment <span> <span>( [-1,1] )</span> </span>, an asymptotic expression for the majorant of uniform approximations, and the optimal values of the parameter of the approximant providing the greatest decrease rate of the majorant. We separately study the approximation properties of the Riesz–Zygmund sums for Fourier–Chebyshev polynomial series, establish an asymptotic expression for the Lebesgue constants, and estimate approximations to <span> <span>( fin H^{(gamma)}[-1,1] )</span> </span> and <span> <span>( gammain(0,1] )</span> </span> as well as pointwise and uniform approximations to the function <span> <span>( |x|^{s} )</span> </span> with <span> <span>( sin(0,2) )</span> </span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"29 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769629","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
Boolean Valued Analysis of Banach Spaces 巴拿赫空间的布尔值分析
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-01-01 DOI: 10.1134/s0037446624010178
{"title":"Boolean Valued Analysis of Banach Spaces","authors":"","doi":"10.1134/s0037446624010178","DOIUrl":"https://doi.org/10.1134/s0037446624010178","url":null,"abstract":"<h3>Abstract</h3> <p>We implement the Boolean valued analysis of Banach spaces. The realizations of Banach spaces in a Boolean valued universe are lattice normed spaces. We present the basic techniques of studying these objects as well as the Boolean valued approach to injective Banach lattices.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"308 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769794","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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