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Short $mathrm{SL}_2$-structures on simple Lie algebras 简单李代数上的短$ mathm {SL}_2$-结构
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9788e
Roman Olegovich Stasenko
{"title":"Short $mathrm{SL}_2$-structures on simple Lie algebras","authors":"Roman Olegovich Stasenko","doi":"10.4213/sm9788e","DOIUrl":"https://doi.org/10.4213/sm9788e","url":null,"abstract":"In Vinberg's works certain non-Abelian gradings of simple Lie algebras were introduced and investigated, namely, short $mathrm{SO}_3$- and $mathrm{SL}_3$-structures. We investigate a different kind of these, short $mathrm{SL}_2$-structures. The main results refer to the one-to-one correspondence between such structures and certain special Jordan algebras. Bibliography: 8 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136302014","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
‘Far interaction’ of small spectral perturbations of the Neumann boundary conditions for an elliptic system of differential equations in a three-dimensional domain 三维域椭圆型微分方程组的小谱摄动的“远相互作用”
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9733e
S. Nazarov
{"title":"‘Far interaction’ of small spectral perturbations of the Neumann boundary conditions for an elliptic system of differential equations in a three-dimensional domain","authors":"S. Nazarov","doi":"10.4213/sm9733e","DOIUrl":"https://doi.org/10.4213/sm9733e","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84200825","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
Bernstein-Szegő inequality for the Riesz derivative of trigonometric polynomials in $L_p$-spaces, $0le pleinfty$, with classical value of the sharp constant 具有锐常数经典值的$L_p$ -空间$0le pleinfty$中三角多项式的Riesz导数的bernstein - szeger不等式
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9822e
Anastasiya Olegovna Leont'eva
{"title":"Bernstein-Szegő inequality for the Riesz derivative of trigonometric polynomials in $L_p$-spaces, $0le pleinfty$, with classical value of the sharp constant","authors":"Anastasiya Olegovna Leont'eva","doi":"10.4213/sm9822e","DOIUrl":"https://doi.org/10.4213/sm9822e","url":null,"abstract":"The Bernstein-Szegő inequality for the Weyl derivative of real order $alphage 0$ of trigonometric polynomials of degree $n$ is considered. The aim is to find values of the parameters for which the sharp constant in this inequality is equal to $n^alpha$ (the classical value) in all $L_p$-spaces, $0le pleinfty$. The set of all such $alpha$ is described for some important particular cases of the Weyl-Szegő derivative, namely, for the Riesz derivative and for the conjugate Riesz derivative, for all $ninmathbb N$. Bibliography: 22 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135596964","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
Regularization of distributions 分布的正则化
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9803e
Aleksandr Leonidovich Pavlov
{"title":"Regularization of distributions","authors":"Aleksandr Leonidovich Pavlov","doi":"10.4213/sm9803e","DOIUrl":"https://doi.org/10.4213/sm9803e","url":null,"abstract":"Sufficient conditions are presented for the construction of a regularization of a distribution in the form $a(sigma)f$, where $f$ is a distribution and $a(sigma)$ is an infinitely differentiable function outside a closed set $N$ which has power-like singularities of derivatives on $N$. Applications of such regularizations to an effective construction of solutions of the equation $Pu=f$, where $P(sigma)$ is a polynomial, are considered. Bibliography: 14 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136302356","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 refinement of Heath-Brown's theorem on quadratic forms 关于二次型的Heath-Brown定理的一个改进
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9711e
Andrey Dymov, Sergei Kuksin, Alberto Maiocchi, Sergei Vladuts
{"title":"A refinement of Heath-Brown's theorem on quadratic forms","authors":"Andrey Dymov, Sergei Kuksin, Alberto Maiocchi, Sergei Vladuts","doi":"10.4213/sm9711e","DOIUrl":"https://doi.org/10.4213/sm9711e","url":null,"abstract":"In his paper from 1996 on quadratic forms Heath-Brown developed a version of the circle method to count points in the intersection of an unbounded quadric with a lattice of small period, when each point is assigned a weight, and approximated this quantity by the integral of the weight function against a measure on the quadric. The weight function is assumed to be $C_0^infty$-smooth and vanish near the singularity of the quadric. In our work we allow the weight function to be finitely smooth, not to vanish at the singularity and have an explicit decay at infinity. The paper uses only elementary number theory and is available to readers with no number-theoretic background. Bibliography: 15 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181021","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
On a class of interpolation inequalities on the 2D sphere 二维球面上的一类插值不等式
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9786e
Sergey Vital'evich Zelik, Aleksei Andreevich Ilyin
{"title":"On a class of interpolation inequalities on the 2D sphere","authors":"Sergey Vital'evich Zelik, Aleksei Andreevich Ilyin","doi":"10.4213/sm9786e","DOIUrl":"https://doi.org/10.4213/sm9786e","url":null,"abstract":"We prove estimates for the $L^p$-norms of systems of functions and divergence-free vector functions that are orthonormal in the Sobolev space $H^1$ on the 2D sphere. As a corollary, order sharp constants for the embedding $H^1hookrightarrow L^q$, $q<infty$, are obtained in the Gagliardo-Nirenberg interpolation inequalities. Bibliography: 25 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135596958","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
Diophantine exponents of lattices and the growth of higher-dimensional analogues of partial quotients 格的丢番图指数和部分商的高维类似物的增长
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9746e
Elmir Rufkatovich Bigushev, Oleg Nikolaevich German
{"title":"Diophantine exponents of lattices and the growth of higher-dimensional analogues of partial quotients","authors":"Elmir Rufkatovich Bigushev, Oleg Nikolaevich German","doi":"10.4213/sm9746e","DOIUrl":"https://doi.org/10.4213/sm9746e","url":null,"abstract":"A three-dimensional analogue of the connection between the exponent of the irrationality of a real number and the growth of the partial quotients of its expansion in a simple continued fraction is investigated. As a multidimensional generalization of continued fractions, Klein polyhedra are considered. Bibliography: 12 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135596974","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
Geometric progression stabilizer in a general metric 一般度规的几何级数稳定器
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9782e
Semeon Antonovich Bogatyi
{"title":"Geometric progression stabilizer in a general metric","authors":"Semeon Antonovich Bogatyi","doi":"10.4213/sm9782e","DOIUrl":"https://doi.org/10.4213/sm9782e","url":null,"abstract":"So-called normalized metrics are considered on the set of elements of a geometric progression. A full description of normalized metrics with maximal stabilizer, which is the group of integer degrees of the common ratio of the progression, is presented. Previously, it was known that this group is the stabilizer for the minimal normalized metric (inherited from the real line) and the maximal normalized metric (an intrinsic metric all paths in which pass through zero). The stabilizer of a metric space is understood as the set of positive numbers such that multiplying the metric by this number produces a metric space lying at a finite Gromov-Hausdorff distance from the original space. Bibliography: 5 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135596976","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
Some classes of almost Hermitian structures that can be realized on $S^6$ 可以在$S^6$上实现的几类几乎厄米结构
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9830e
Nataliya Aleksandrovna Daurtseva
{"title":"Some classes of almost Hermitian structures that can be realized on $S^6$","authors":"Nataliya Aleksandrovna Daurtseva","doi":"10.4213/sm9830e","DOIUrl":"https://doi.org/10.4213/sm9830e","url":null,"abstract":"Structures of cohomogeneity one on $S^6$ are under investigation. Examples of semi-Kähler and quasi-Kähler structures are constructed. Questions concerning the existence of almost Hermitian structures of cohomogeneity one on a round sphere are investigated. Bibliography: 14 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134982655","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
[IMG align=ABSMIDDLE alt=$ p$]tex_sm_5014_img1[/IMG]-convexity functor for [IMG align=ABSMIDDLE alt=$ L_p(X)$]tex_sm_5014_img2[/IMG]-spaces [IMG align=ABSMIDDLE alt=$ p$]tex_sm_5014_img1[/IMG]- [IMG align=ABSMIDDLE alt=$ L_p(X)$]tex_sm_5014_img2[/IMG]-空格的凸函子
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/sm9674
N. Volosova
{"title":"[IMG align=ABSMIDDLE alt=$ p$]tex_sm_5014_img1[/IMG]-convexity functor for [IMG align=ABSMIDDLE alt=$ L_p(X)$]tex_sm_5014_img2[/IMG]-spaces","authors":"N. Volosova","doi":"10.1070/sm9674","DOIUrl":"https://doi.org/10.1070/sm9674","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73880676","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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