Pub Date : 1993-02-28DOI: 10.1070/SM1993V074N02ABEH003353
Kh. M. Makhmudov
The author establishes that, for every function that is analytic inside the unit disk and belongs to the space with 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>, the equation is satisfied, where and are the minimal deviations of from polynomials of degree at most and from rational functions of order at most . In particular, if and only if can be continued analytically over the disk .There is also a similar proposition for the approximation of functions in the spaces , 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>.
{"title":"ON FUNCTIONS WITH SIMILAR VALUES FOR MINIMAL DEVIATIONS FROM POLYNOMIALS AND RATIONAL FUNCTIONS","authors":"Kh. M. Makhmudov","doi":"10.1070/SM1993V074N02ABEH003353","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003353","url":null,"abstract":"The author establishes that, for every function that is analytic inside the unit disk and belongs to the space with 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>, the equation is satisfied, where and are the minimal deviations of from polynomials of degree at most and from rational functions of order at most . In particular, if and only if can be continued analytically over the disk .There is also a similar proposition for the approximation of functions in the spaces , 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"8 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":"115499880","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/SM1993V074N02ABEH003361
S. S. Ryshkov, R. M. Èrdal
After giving a brief introduction to our new "theory of dual systems of integer vectors", we give the first applications to the theory of positive quadratic forms. We consider the question of enumerating the L-polytopes of lattices, paying particular attention to the case of five-dimensional lattices. The results reported in this paper were announced earlier by the authors in Doklady [1]; here we give the details.
{"title":"DUAL SYSTEMS OF INTEGER VECTORS (GENERAL QUESTIONS AND APPLICATIONS TO THE GEOMETRY OF POSITIVE QUADRATIC FORMS)","authors":"S. S. Ryshkov, R. M. Èrdal","doi":"10.1070/SM1993V074N02ABEH003361","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003361","url":null,"abstract":"After giving a brief introduction to our new \"theory of dual systems of integer vectors\", we give the first applications to the theory of positive quadratic forms. We consider the question of enumerating the L-polytopes of lattices, paying particular attention to the case of five-dimensional lattices. The results reported in this paper were announced earlier by the authors in Doklady [1]; here we give the details.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"103 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":"127135344","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/SM1993V074N02ABEH003360
V. A. Lyubishkin
A connection is established between the well-known trace formulas of Gel'fand-Levitan and Kreĭn.
在著名的Gel'fand-Levitan微量公式和Kreĭn之间建立了联系。
{"title":"ON THE TRACE FORMULAS OF GEL'FAND-LEVITAN AND KREĬN","authors":"V. A. Lyubishkin","doi":"10.1070/SM1993V074N02ABEH003360","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003360","url":null,"abstract":"A connection is established between the well-known trace formulas of Gel'fand-Levitan and Kreĭn.","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":"114593789","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/SM1993V074N01ABEH003338
A. D’yachkov
The set of Lebesgue points of a locally integrable function on -dimensional Euclidean space , , is an -set of full measure. In this article it is shown that every -set of full measure is the set of Lebesgue points of some measurable bounded function, and, further, that a set with these properties is the set of points of convergence and nontangential (stable) convergence of a singular integral of convolution type: for some measurable bounded function . On the basis of this result the set of points of summability of a multiple Fourier series by methods of Abel, Riesz, and Picard types is described.
{"title":"A DESCRIPTION OF THE SETS OF LEBESGUE POINTS AND POINTS OF SUMMABILITY OF A FOURIER SERIES","authors":"A. D’yachkov","doi":"10.1070/SM1993V074N01ABEH003338","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003338","url":null,"abstract":"The set of Lebesgue points of a locally integrable function on -dimensional Euclidean space , , is an -set of full measure. In this article it is shown that every -set of full measure is the set of Lebesgue points of some measurable bounded function, and, further, that a set with these properties is the set of points of convergence and nontangential (stable) convergence of a singular integral of convolution type: for some measurable bounded function . On the basis of this result the set of points of summability of a multiple Fourier series by methods of Abel, Riesz, and Picard types is described.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"18 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":"134512172","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/SM1993V074N02ABEH003359
M. Vishik, M. Skvortsov
In a domain we consider the first boundary value problem for a quasilinear parabolic fourth-order equation with a small parameter in the highest derivatives, which degenerates for into a second order equation. It is well known that the semigroup corresponding to this problem has an attractor, that is, an invariant attracting set in the phase space. In this paper we investigate the structure of this attractor by means of an asymptotic expansion in .The dominant term of the asymptotics is the solution of a second-order equation. The asymptotic expansion also contains boundary layer functions, which are responsible for the deterioration of the differential properties of the elements of the attractor near the boundary. The asymptotics constructed in this way (with an estimate of the remainder) enable us to study the differential properties of attractors and their behavior as in any interior subdomain , .For simplicity, the investigation is carried out in the case when is a bounded cylindrical domain. The generalization to does not present any difficulties.
{"title":"ASYMPTOTICS OF THE ELEMENTS OF ATTRACTORS CORRESPONDING TO SINGULARLY PERTURBED PARABOLIC EQUATIONS","authors":"M. Vishik, M. Skvortsov","doi":"10.1070/SM1993V074N02ABEH003359","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003359","url":null,"abstract":"In a domain we consider the first boundary value problem for a quasilinear parabolic fourth-order equation with a small parameter in the highest derivatives, which degenerates for into a second order equation. It is well known that the semigroup corresponding to this problem has an attractor, that is, an invariant attracting set in the phase space. In this paper we investigate the structure of this attractor by means of an asymptotic expansion in .The dominant term of the asymptotics is the solution of a second-order equation. The asymptotic expansion also contains boundary layer functions, which are responsible for the deterioration of the differential properties of the elements of the attractor near the boundary. The asymptotics constructed in this way (with an estimate of the remainder) enable us to study the differential properties of attractors and their behavior as in any interior subdomain , .For simplicity, the investigation is carried out in the case when is a bounded cylindrical domain. The generalization to does not present any difficulties.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"3 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":"128658798","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/SM1993V074N02ABEH003358
V. Zvyagin
The concept of oriented degree is extended to the class of mappings of the form f – g, where f is a proper Fredholm mapping of nonnegative index and g a continuous f-compactly restrictable mapping. In the case when f is a Fredholm mapping of zero index and f and g are equivariant with respect to the action of the circle and the torus, formulas are obtained which express the degree of these mappings in terms of invariants of representations of the corresponding groups. An application to the investigation of the global behavior of a bifurcation branch of a certain nonlinear boundary value problem is given.
{"title":"ON THE ORIENTED DEGREE OF A CERTAIN CLASS OF PERTURBATIONS OF FREDHOLM MAPPINGS, AND ON BIFURCATION OF SOLUTIONS OF A NONLINEAR BOUNDARY VALUE PROBLEM WITH NONCOMPACT PERTURBATIONS","authors":"V. Zvyagin","doi":"10.1070/SM1993V074N02ABEH003358","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003358","url":null,"abstract":"The concept of oriented degree is extended to the class of mappings of the form f – g, where f is a proper Fredholm mapping of nonnegative index and g a continuous f-compactly restrictable mapping. In the case when f is a Fredholm mapping of zero index and f and g are equivariant with respect to the action of the circle and the torus, formulas are obtained which express the degree of these mappings in terms of invariants of representations of the corresponding groups. An application to the investigation of the global behavior of a bifurcation branch of a certain nonlinear boundary value problem is given.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"84 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":"126234245","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/SM1993V074N01ABEH003333
A. Dranishnikov
It is determined under what conditions the standard problem of extension of a mapping to the whole space is solvable for any closed subset . For finite-dimensional metric compacta and -complexes this is equivalent to the system of inequalities -. The result is applied to finding conditions for general position of a compactum in a Euclidean space.
{"title":"EXTENSION OF MAPPINGS INTO $ mathrm{CW}$-COMPLEXES","authors":"A. Dranishnikov","doi":"10.1070/SM1993V074N01ABEH003333","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003333","url":null,"abstract":"It is determined under what conditions the standard problem of extension of a mapping to the whole space is solvable for any closed subset . For finite-dimensional metric compacta and -complexes this is equivalent to the system of inequalities -. The result is applied to finding conditions for general position of a compactum in a Euclidean space.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"259 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":"123081548","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/SM1993V074N02ABEH003351
N. K. Rakhmetov
This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces and on the interval , where is an even nonnegative continuous nondecreasing function on the half-line , and the function is measurable, finite, and positive almost everywhere on . If is an -function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm.
{"title":"ON FINITE-DIMENSIONAL CHEBYSHEV SUBSPACES OF SPACES WITH AN INTEGRAL METRIC","authors":"N. K. Rakhmetov","doi":"10.1070/SM1993V074N02ABEH003351","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003351","url":null,"abstract":"This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces and on the interval , where is an even nonnegative continuous nondecreasing function on the half-line , and the function is measurable, finite, and positive almost everywhere on . If is an -function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"30 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":"122665291","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/SM1993V074N01ABEH003336
V. M. Shiryaev
A semigroup is called filtering if each of its subsemigroups has the smallest (with respect to inclusion) generating set. It is proved in this article that every maximal chain of nonempty subsemigroups of a finite filtering semigroup has length equal to the order of the semigroup, and that filtering semigroups are characterized by this property in the class of finite semigroups. The main result is a characterization of the class of finite filtering semigroups by means of forbidden divisors, to which end the author finds all finite nonfiltering semigroups all of whose proper divisors are filtering semigroups.
{"title":"FINITE FILTERING SEMIGROUPS","authors":"V. M. Shiryaev","doi":"10.1070/SM1993V074N01ABEH003336","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003336","url":null,"abstract":"A semigroup is called filtering if each of its subsemigroups has the smallest (with respect to inclusion) generating set. It is proved in this article that every maximal chain of nonempty subsemigroups of a finite filtering semigroup has length equal to the order of the semigroup, and that filtering semigroups are characterized by this property in the class of finite semigroups. The main result is a characterization of the class of finite filtering semigroups by means of forbidden divisors, to which end the author finds all finite nonfiltering semigroups all of whose proper divisors are filtering semigroups.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"27 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":"122325126","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/SM1993V074N01ABEH003337
I. Shestakov
It is proved that any prime Malcev superalgebra of characteristic 2, 3 with nonzero odd part is a Lie superalgebra.
证明了任何特征为2,3且奇部非零的素数Malcev超代数都是李超代数。
{"title":"PRIME MALCEV SUPERALGEBRAS","authors":"I. Shestakov","doi":"10.1070/SM1993V074N01ABEH003337","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003337","url":null,"abstract":"It is proved that any prime Malcev superalgebra of characteristic 2, 3 with nonzero odd part is a Lie superalgebra.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"13 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":"134359493","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}
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