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Mathematics of The Ussr-sbornik最新文献

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MEAN DIMENSION, WIDTHS, AND OPTIMAL RECOVERY OF SOBOLEV CLASSES OF FUNCTIONS ON THE LINE 平均维数，宽度，和最优恢复的索波列夫类的函数对线
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N02ABEH003352
G. Magaril-Il'yaev
{"title":"MEAN DIMENSION, WIDTHS, AND OPTIMAL RECOVERY OF SOBOLEV CLASSES OF FUNCTIONS ON THE LINE","authors":"G. Magaril-Il'yaev","doi":"10.1070/SM1993V074N02ABEH003352","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003352","url":null,"abstract":"The concept of mean dimension is introduced for a broad class of subspaces of , and analogues of the Kolmogorov widths, Bernstein widths, Gel'fand widths, and linear widths are defined. The precise values of these quantities are computed for Sobolev classes of functions on in compatible metrics, and the corresponding extremal spaces and operators are described. A closely related problem of optimal recovery of functions in Sobolev classes is also studied.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"42 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":"130282076","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}
引用次数: 19
NUMERICAL RESULTS ON BEST UNIFORM RATIONAL APPROXIMATION OF $ vert xvert$ ON $ lbrack-1,,+1rbrack$ $ vert xvert$在$ rbrack$，，+1rbrack$上的最佳一致有理逼近的数值结果
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N02ABEH003347
R. Varga, A. Ruttan, A. D. Karpenter
{"title":"NUMERICAL RESULTS ON BEST UNIFORM RATIONAL APPROXIMATION OF $ vert xvert$ ON $ lbrack-1,,+1rbrack$","authors":"R. Varga, A. Ruttan, A. D. Karpenter","doi":"10.1070/SM1993V074N02ABEH003347","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003347","url":null,"abstract":"With denoting the error of best uniform rational approximation from to on , we determine the numbers , where each of these numbers was calculated with a precision of at least 200 significant digits. With these numbers, the Richardson extrapolation method was applied to the products , and it appears, to at least 10 significant digits, that which gives rise to an interesting new conjecture in the theory of rational approximation.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"1 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":"123006663","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}
引用次数: 11
PROJECTION-NET WIDTHS AND LATTICE PACKINGS 投影网宽度和格子填料
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003346
N. Strelkov
{"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}
引用次数: 1
APPROXIMATIONS OF THE EXPONENTIAL FUNCTION AND RELATIVE CLOSENESS OF STABLE SIGNALS 指数函数的近似和稳定信号的相对接近度
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N02ABEH003348
L. A. Balashov, Y. Dreizin, M. S. Mel'nikov
{"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}
引用次数: 0
RATIONALITY OF FIELDS OF INVARIANTS OF SOME FOUR-DIMENSIONAL LINEAR GROUPS, AND AN EQUIVARIANT CONSTRUCTION RELATED TO THE SEGRE CUBIC 一些四维线性群的不变量域的合理性，以及与分段三次相关的等变构造
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003342
I. Y. Kolpakov-Miroshnichenko, Yuri Prokhorov
{"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}
引用次数: 6
ON THE RATIONALITY PROBLEM FOR CONIC BUNDLES 关于二次束的合理性问题
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V072N01ABEH001264
V. A. Iskovskikh
{"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}
引用次数: 40
ON THE SPECTRUM OF THE OPERATOR PENCIL GENERATED BY THE DIRICHLET PROBLEM IN A CONE 锥上狄利克雷问题产生的算子铅笔谱
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V073N01ABEH002533
V. Kozlov, V. Maz'ya
{"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}
引用次数: 19
ON THE FOURIER-HAAR SERIES OF COMPOSITE FUNCTIONS 复合函数的傅里叶-哈尔级数
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V072N01ABEH002140
V. M. Bugadze
{"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}
引用次数: 5
ON THE POSSIBLE RATE OF GROWTH OF POLYNOMIALS ORTHOGONAL WITH A CONTINUOUS POSITIVE WEIGHT 具有连续正权的正交多项式的可能增长率
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V072N02ABEH001269
M. U. Ambroladze
{"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}
引用次数: 16
ON ARITHMETIC PROPERTIES OF THE VALUES OF HYPERGEOMETRIC FUNCTIONS 超几何函数值的算术性质
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V072N01ABEH001413
P. Ivankov
{"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}
引用次数: 16
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