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A Littlewood-Paley-Rubio de Francia inequality for bounded Vilenkin systems 有界Vilenkin系统的littlewood - paly - rubio de Francia不等式
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9482
A. Tselishchev
{"title":"A Littlewood-Paley-Rubio de Francia inequality for bounded Vilenkin systems","authors":"A. Tselishchev","doi":"10.1070/SM9482","DOIUrl":"https://doi.org/10.1070/SM9482","url":null,"abstract":"Rubio de Francia proved a one-sided Littlewood-Paley inequality for the square function constructed from an arbitrary system of disjoint intervals. Later, Osipov proved a similar inequality for Walsh systems. We prove a similar inequality for more general Vilenkin systems. Bibliography: 11 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77541600","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: 5
Asymptotics of the scattering operator for the wave equation in a singularly perturbed domain 奇摄动区域波动方程散射算子的渐近性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9462
D. Korikov
{"title":"Asymptotics of the scattering operator for the wave equation in a singularly perturbed domain","authors":"D. Korikov","doi":"10.1070/SM9462","DOIUrl":"https://doi.org/10.1070/SM9462","url":null,"abstract":"A family of Cauchy-Dirichlet problems for the wave equations in unbounded domains is considered (here is a small parameter); a scattering operator is associated with each domain . For 0$?> the boundaries of the are smooth, while the boundary of the limit domain contains a conical point. The asymptotics of as is determined. Bibliography: 11 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81537971","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
Characterization of solutions of strong-weak convex programming problems 强-弱凸规划问题解的表征
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9431
S. Dudov, M. Osiptsev
{"title":"Characterization of solutions of strong-weak convex programming problems","authors":"S. Dudov, M. Osiptsev","doi":"10.1070/SM9431","DOIUrl":"https://doi.org/10.1070/SM9431","url":null,"abstract":"Finite-dimensional problems of minimizing a strongly or weakly convex function on a strongly or weakly convex set are considered. Necessary and sufficient conditions for solutions of such problems are presented, which are based on estimates for the behaviour of the objective function on the feasible set taking account of the parameters of strong or weak convexity, as well as certain local features of the set and the function. The mathematical programming problem is considered separately for strongly and weakly convex functions. In addition, necessary conditions for a global and a local solution with differentiable objective function are found, in which a ‘strong’ stationarity condition is assumed to hold. Bibliography: 33 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83602437","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: 1
A probability estimate for the discrepancy of Korobov lattice points Korobov格点差异的概率估计
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9522
A. A. Illarionov
{"title":"A probability estimate for the discrepancy of Korobov lattice points","authors":"A. A. Illarionov","doi":"10.1070/SM9522","DOIUrl":"https://doi.org/10.1070/SM9522","url":null,"abstract":"Bykovskii (2002) obtained the best current upper estimate for the minimum discrepancy of the Korobov lattice points from the uniform distribution. We show that this estimate holds for almost all -dimensional Korobov lattices of nodes, where , and is a prime number. Bibliography: 14 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80309227","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
Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms 小正则同胚共轭的充分必要条件
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9244
E. Zhuzhoma, V. Medvedev
{"title":"Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms","authors":"E. Zhuzhoma, V. Medvedev","doi":"10.1070/SM9244","DOIUrl":"https://doi.org/10.1070/SM9244","url":null,"abstract":"The class of Smale regular homeomorphisms of closed topological manifolds, with nonwandering set consisting of a finite number of periodic orbits of hyperbolic type, is considered. This class contains the Morse-Smale diffeomorphisms of smooth closed manifolds. For two Smale regular homomorphisms necessary and sufficient conditions for being conjugate are presented. Bibliography: 26 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88863853","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: 2
Mironov Lagrangian cycles in algebraic varieties 代数变异中的Mironov拉格朗日循环
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9407
N. Tyurin
{"title":"Mironov Lagrangian cycles in algebraic varieties","authors":"N. Tyurin","doi":"10.1070/SM9407","DOIUrl":"https://doi.org/10.1070/SM9407","url":null,"abstract":"We generalize a construction due to Mironov. Some time ago he presented new examples of minimal and Hamiltonian minimal Lagrangian submanifolds in and . His construction is based on the considerations of a noncomplete toric action of , where , on subspaces that are invariant with respect to the action of a natural antiholomorphic involution. This situation takes place for a rather broad class of algebraic varieties: complex quadrics, Grassmannians, flag varieties and so on, which makes it possible to construct many new examples of Lagrangian submanifolds in these algebraic varieties. Bibliography: 4 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86371116","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: 2
Uniqueness theorems for simple trigonometric series with application to multiple series 简单三角级数的唯一性定理及其在多重级数中的应用
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9525
G. G. Gevorkyan
{"title":"Uniqueness theorems for simple trigonometric series with application to multiple series","authors":"G. G. Gevorkyan","doi":"10.1070/SM9525","DOIUrl":"https://doi.org/10.1070/SM9525","url":null,"abstract":"For simple trigonometric series it is shown, in particular, that if the trigonometric series is Riemann summable in measure to an integrable function and if the Riemann majorant is finite everywhere except possibly on a countable set, then this series is the Fourier series of the function . Uniqueness theorems for multiple trigonometric series are obtained on the basis of this result. Bibliography: 14 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89815484","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: 1
Global and semilocal theorems on implicit and inverse functions in Banach spaces Banach空间中隐函数和逆函数的整体和半局部定理
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9483
A. Arutyunov, S. Zhukovskiy
{"title":"Global and semilocal theorems on implicit and inverse functions in Banach spaces","authors":"A. Arutyunov, S. Zhukovskiy","doi":"10.1070/SM9483","DOIUrl":"https://doi.org/10.1070/SM9483","url":null,"abstract":"We consider continuous mappings between two Banach spaces that depend on a parameter with values in a topological space. These mappings are assumed to be continuously differentiable for each value of the parameter. Under normality (regularity) assumptions of the mappings under consideration, we obtain sufficient conditions for the existence of global and semilocal implicit functions. A priori estimates for solutions are given. As an application of these results, we obtain, in particular, a theorem on extending an implicit function from a given closed set to the whole parameter space and a theorem on coincidence points of mappings. Bibliography: 32 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79366916","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: 4
On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution 论时滞解的支点收缩现象及解的消光
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9377
S. P. Degtyarev
{"title":"On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution","authors":"S. P. Degtyarev","doi":"10.1070/SM9377","DOIUrl":"https://doi.org/10.1070/SM9377","url":null,"abstract":"The phenomenon of support shrinking with a time delay for the solution of a doubly nonlinear degenerate parabolic equation is studied in the case of slow diffusion and strong absorption. For a nonnegative solution, a sufficient condition for support shrinking beginning with some moment of time is deduced in terms of the local behaviour of the mass of the initial datum. It is also proved that the solution vanishes identically in finite time. Bibliography: 21 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81831635","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 optimal recovery of values of linear operators from information known with a stochastic error 具有随机误差的已知信息中线性算子值的最优恢复
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9484
K. Y. Krivosheev
{"title":"On optimal recovery of values of linear operators from information known with a stochastic error","authors":"K. Y. Krivosheev","doi":"10.1070/SM9484","DOIUrl":"https://doi.org/10.1070/SM9484","url":null,"abstract":"The optimal recovery of values of linear operators is considered for classes of elements the information on which is known with a stochastic error. Linear optimal recovery methods are constructed that, in general, do not use all the available information for the measurements. As a consequence, an optimal method is described for recovering a function from a finite set of its Fourier coefficients specified with a stochastic error. Bibliography: 14 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88610428","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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