Pub Date : 1993-02-28DOI: 10.1070/SM1993V074N01ABEH003346
N. Strelkov
Problems of approximation in a class of function spaces, including Sobolev spaces, by subspaces of finite-element type generated by translations of a lattice of given functions are considered. Widths that describe the approximation properties of such subspaces are defined, and their exact values are enumerated. Necessary and sufficient conditions are obtained for the optimality of subspaces on which these widths are realized. Criteria for the optimality of lattices in terms of the density of lattice packings of certain functions (for Sobolev spaces, of densities of packings by identical spheres) are established. Problems of comparison of the widths used in this article with the Kolmogorov widths of the same mean dimension are discussed.
{"title":"PROJECTION-NET WIDTHS AND LATTICE PACKINGS","authors":"N. Strelkov","doi":"10.1070/SM1993V074N01ABEH003346","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003346","url":null,"abstract":"Problems of approximation in a class of function spaces, including Sobolev spaces, by subspaces of finite-element type generated by translations of a lattice of given functions are considered. Widths that describe the approximation properties of such subspaces are defined, and their exact values are enumerated. Necessary and sufficient conditions are obtained for the optimality of subspaces on which these widths are realized. Criteria for the optimality of lattices in terms of the density of lattice packings of certain functions (for Sobolev spaces, of densities of packings by identical spheres) are established. Problems of comparison of the widths used in this article with the Kolmogorov widths of the same mean dimension are discussed.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131443270","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}
Pub Date : 1993-02-28DOI: 10.1070/SM1993V074N02ABEH003348
L. A. Balashov, Y. Dreizin, M. S. Mel'nikov
The results presented here are based on the use of approximations of analytic functions in certain questions involving numerical methods for physical equations. The concepts of relative closeness and of stability of signals are introduced. A simple method is given for approximate inversion of the Laplace transformation, with an estimate of the relative error. Also, estimates are obtained for the dimensions of spaces in which it is possible to find approximate solutions of multidimensional systems of linear equations, as a function of the accuracy of approximation and the size of the spectrum of the operator.
{"title":"APPROXIMATIONS OF THE EXPONENTIAL FUNCTION AND RELATIVE CLOSENESS OF STABLE SIGNALS","authors":"L. A. Balashov, Y. Dreizin, M. S. Mel'nikov","doi":"10.1070/SM1993V074N02ABEH003348","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003348","url":null,"abstract":"The results presented here are based on the use of approximations of analytic functions in certain questions involving numerical methods for physical equations. The concepts of relative closeness and of stability of signals are introduced. A simple method is given for approximate inversion of the Laplace transformation, with an estimate of the relative error. Also, estimates are obtained for the dimensions of spaces in which it is possible to find approximate solutions of multidimensional systems of linear equations, as a function of the accuracy of approximation and the size of the spectrum of the operator.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125762513","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}
Pub Date : 1993-02-28DOI: 10.1070/SM1993V074N01ABEH003342
I. Y. Kolpakov-Miroshnichenko, Yuri Prokhorov
Let be a finite primitive linear group. We prove that if contains a normal subgroup of order 32 then the quotient variety is birationally isomorphic to , where is the Segre cubic. We also prove the rationality of for a large class of such groups (in particular, solvable groups).
{"title":"RATIONALITY OF FIELDS OF INVARIANTS OF SOME FOUR-DIMENSIONAL LINEAR GROUPS, AND AN EQUIVARIANT CONSTRUCTION RELATED TO THE SEGRE CUBIC","authors":"I. Y. Kolpakov-Miroshnichenko, Yuri Prokhorov","doi":"10.1070/SM1993V074N01ABEH003342","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003342","url":null,"abstract":"Let be a finite primitive linear group. We prove that if contains a normal subgroup of order 32 then the quotient variety is birationally isomorphic to , where is the Segre cubic. We also prove the rationality of for a large class of such groups (in particular, solvable groups).","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"175 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126177646","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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V072N01ABEH001264
V. A. Iskovskikh
For a standard conic bundle over a rational surface the equivalence of two different pairs of conditions sufficient for rationality is proved, along with the necessity of certain weaker conditions.
对于有理曲面上的标准圆锥束，证明了两对不同条件的等价性，并证明了若干较弱条件的必要性。
{"title":"ON THE RATIONALITY PROBLEM FOR CONIC BUNDLES","authors":"V. A. Iskovskikh","doi":"10.1070/SM1992V072N01ABEH001264","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001264","url":null,"abstract":"For a standard conic bundle over a rational surface the equivalence of two different pairs of conditions sufficient for rationality is proved, along with the necessity of certain weaker conditions.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115815680","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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N01ABEH002533
V. Kozlov, V. Maz'ya
The operator pencil whose eigenvalues determine singularities of solutions to the Dirichlet problem at the vertex of a cone is studied. First the Dirichlet-Sobolev problem with data on the ray is considered, and the eigenvalues and eigenfunctions of the corresponding operator pencil are described. Then this information is used to show that the result of [2] is best possible in a sense.
{"title":"ON THE SPECTRUM OF THE OPERATOR PENCIL GENERATED BY THE DIRICHLET PROBLEM IN A CONE","authors":"V. Kozlov, V. Maz'ya","doi":"10.1070/SM1992V073N01ABEH002533","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002533","url":null,"abstract":"The operator pencil whose eigenvalues determine singularities of solutions to the Dirichlet problem at the vertex of a cone is studied. First the Dirichlet-Sobolev problem with data on the ray is considered, and the eigenvalues and eigenfunctions of the corresponding operator pencil are described. Then this information is used to show that the result of [2] is best possible in a sense.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117057985","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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V072N01ABEH002140
V. M. Bugadze
The author determines the class of all homeomorphic changes of variable that preserve absolute convergence of the series of Fourier-Haar coefficients.It is established that among all the continuously differentiable homeomorphic changes of variable only the functions and defined by the equalities and for preserve both convergence and absolute convergence of the Fourier-Haar series.The class of Borel measurable functions whose Fourier-Haar series converge everywhere under any homeomorphic change of variable is determined, along with the class of all Borel measurable functions whose Fourier-Haar series converge absolutely at every point under any homeomorphic change of variable.
{"title":"ON THE FOURIER-HAAR SERIES OF COMPOSITE FUNCTIONS","authors":"V. M. Bugadze","doi":"10.1070/SM1992V072N01ABEH002140","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH002140","url":null,"abstract":"The author determines the class of all homeomorphic changes of variable that preserve absolute convergence of the series of Fourier-Haar coefficients.It is established that among all the continuously differentiable homeomorphic changes of variable only the functions and defined by the equalities and for preserve both convergence and absolute convergence of the Fourier-Haar series.The class of Borel measurable functions whose Fourier-Haar series converge everywhere under any homeomorphic change of variable is determined, along with the class of all Borel measurable functions whose Fourier-Haar series converge absolutely at every point under any homeomorphic change of variable.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117063134","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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V072N02ABEH001269
M. U. Ambroladze
It is proved that there are continuous positive weights such that the orthogonal polynomials constructed with respect to them are not uniformly bounded at a given point, both for the circle and for a closed interval. Furthermore, in the case of the circle the orthogonal polynomials have logarithmic growth. Also determined is a minimal (in a certain sense) class of positive continuous functions in which there exists a weight function having the property indicated.
{"title":"ON THE POSSIBLE RATE OF GROWTH OF POLYNOMIALS ORTHOGONAL WITH A CONTINUOUS POSITIVE WEIGHT","authors":"M. U. Ambroladze","doi":"10.1070/SM1992V072N02ABEH001269","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH001269","url":null,"abstract":"It is proved that there are continuous positive weights such that the orthogonal polynomials constructed with respect to them are not uniformly bounded at a given point, both for the circle and for a closed interval. Furthermore, in the case of the circle the orthogonal polynomials have logarithmic growth. Also determined is a minimal (in a certain sense) class of positive continuous functions in which there exists a weight function having the property indicated.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117347430","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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V072N01ABEH001413
P. Ivankov
The author proposes an effective method of constructing a linear approximating form for a hypergeometric function of general type and its derivatives, which has a zero of the maximal possible order at z = 0. This construction is applied to the study of arithmetic properties of values of these functions at points of an imaginary quadratic field.
{"title":"ON ARITHMETIC PROPERTIES OF THE VALUES OF HYPERGEOMETRIC FUNCTIONS","authors":"P. Ivankov","doi":"10.1070/SM1992V072N01ABEH001413","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001413","url":null,"abstract":"The author proposes an effective method of constructing a linear approximating form for a hypergeometric function of general type and its derivatives, which has a zero of the maximal possible order at z = 0. This construction is applied to the study of arithmetic properties of values of these functions at points of an imaginary quadratic field.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"18 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123280593","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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N02ABEH001401
V. Zharinov
A number of properties of differential algebras are determined, and on that basis a connection between conservation laws of nonlinear nonregular systems of partial differential equations and properties of a special class of differential operators is found.
{"title":"DIFFERENTIAL ALGEBRAS AND LOW-DIMENSIONAL CONSERVATION LAWS","authors":"V. Zharinov","doi":"10.1070/SM1992V071N02ABEH001401","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001401","url":null,"abstract":"A number of properties of differential algebras are determined, and on that basis a connection between conservation laws of nonlinear nonregular systems of partial differential equations and properties of a special class of differential operators is found.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126599071","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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N02ABEH002134
V. Shlyk
A study is made of the properties of -normal domains in (), which will be minimal in the Koebe sense or normal in the Grotzsch sense when . Descriptions are obtained of removable singularities for the space and for compact sets generating -normal domains, in terms of the theory of contingencies and -dimensional bi-Lipschitz -compact sets.
{"title":"THE STRUCTURE OF COMPACT SETS GENERATING NORMAL DOMAINS, AND REMOVABLE SINGULARITIES FOR THE SPACE $ L_p^1(D)$","authors":"V. Shlyk","doi":"10.1070/SM1992V071N02ABEH002134","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH002134","url":null,"abstract":"A study is made of the properties of -normal domains in (), which will be minimal in the Koebe sense or normal in the Grotzsch sense when . Descriptions are obtained of removable singularities for the space and for compact sets generating -normal domains, in terms of the theory of contingencies and -dimensional bi-Lipschitz -compact sets.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126730697","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：