Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N02ABEH002135
K. K. Boimatov, A. G. Kostyuchenko
In a bounded domain with smooth boundary, a matrix elliptic differential operator is considered. It is assumed that the eigenvalues of the symbol of lie on the positive semiaxis and outside the angle , .The principal term of the asymptotics of the function describing the distribution of the eigenvalues of in the angle is calculated. Under the condition that all the eigenvalues of the symbol lie outside , upper bounds are obtained for with reduced order of growth. The case of a selfadjoint operator is considered separately.
{"title":"SPECTRAL ASYMPTOTICS OF NONSELFADJOINT ELLIPTIC SYSTEMS OF DIFFERENTIAL OPERATORS IN BOUNDED DOMAINS","authors":"K. K. Boimatov, A. G. Kostyuchenko","doi":"10.1070/SM1992V071N02ABEH002135","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH002135","url":null,"abstract":"In a bounded domain with smooth boundary, a matrix elliptic differential operator is considered. It is assumed that the eigenvalues of the symbol of lie on the positive semiaxis and outside the angle , .The principal term of the asymptotics of the function describing the distribution of the eigenvalues of in the angle is calculated. Under the condition that all the eigenvalues of the symbol lie outside , upper bounds are obtained for with reduced order of growth. The case of a selfadjoint operator is considered separately.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"133 9 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":"124254735","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/SM1992V073N01ABEH002536
S. Nazarov
A complete asymptotic expansion is found for the solution of the Dirichlet problem for a second-order scalar equation in a rectangle. The exponents of the powers of in the series are (generally speaking, nonintegral) nonnegative numbers of the form , where , , and is the opening of the angle which is transformed into a quarter plane under the change of coordinates taking the Laplace operator into the principal part of the averaged operator at the vertex of the rectangle. The coefficients of the series for rational may depend in polynomial fashion on . It is shown that the algorithm also does not change in the case of a system of differential equations or in the case of a domain bounded by polygonal lines with vertices at the nodes of an -lattice. The spectral problem is considered; asymptotic formulas for the eigenvalue and the eigenfunction are obtained under the assumption that is a simple eigenvalue of the averaged Dirichlet problem.
{"title":"ASYMPTOTICS OF THE SOLUTION OF THE DIRICHLET PROBLEM FOR AN EQUATION WITH RAPIDLY OSCILLATING COEFFICIENTS IN A RECTANGLE","authors":"S. Nazarov","doi":"10.1070/SM1992V073N01ABEH002536","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002536","url":null,"abstract":"A complete asymptotic expansion is found for the solution of the Dirichlet problem for a second-order scalar equation in a rectangle. The exponents of the powers of in the series are (generally speaking, nonintegral) nonnegative numbers of the form , where , , and is the opening of the angle which is transformed into a quarter plane under the change of coordinates taking the Laplace operator into the principal part of the averaged operator at the vertex of the rectangle. The coefficients of the series for rational may depend in polynomial fashion on . It is shown that the algorithm also does not change in the case of a system of differential equations or in the case of a domain bounded by polygonal lines with vertices at the nodes of an -lattice. The spectral problem is considered; asymptotic formulas for the eigenvalue and the eigenfunction are obtained under the assumption that is a simple eigenvalue of the averaged Dirichlet problem.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"77 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":"131241449","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/SM1992V073N02ABEH002552
P. Naumkin, I. A. Shishmarev
The asymptotics as is constructed for solutions of the Cauchy problem for a nonlinear nonlocal Schrodinger equation.
构造了一类非线性非定域薛定谔方程Cauchy问题解的渐近性。
{"title":"THE ASYMPTOTICS AS $ ttoinfty$ OF SOLUTIONS OF A NONLINEAR NONLOCAL SCHRÖDINGER EQUATION","authors":"P. Naumkin, I. A. Shishmarev","doi":"10.1070/SM1992V073N02ABEH002552","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002552","url":null,"abstract":"The asymptotics as is constructed for solutions of the Cauchy problem for a nonlinear nonlocal Schrodinger equation.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"96 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":"127242787","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/SM1992V071N02ABEH001407
D. V. Prokhorov
The problem of describing the set of values of a system of functional {f(Z), ..., f(n)(Z)} in the class of univalent functions holomorphic in the disk is formalized as a problem of constructing the set of attainability for a control system generated by the Loewner equation. In this problem the maximum principle turns out to be a necessary and sufficient condition for optimality. An algorithm for finding this set for a generalized Loewner equation with constant coefficients and continuous control is constructed. The results are extended to classes of bounded univalent functions.
{"title":"Sets of Values of Systems of Functionals in Classes of Univalent Functions","authors":"D. V. Prokhorov","doi":"10.1070/SM1992V071N02ABEH001407","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001407","url":null,"abstract":"The problem of describing the set of values of a system of functional {f(Z), ..., f(n)(Z)} in the class of univalent functions holomorphic in the disk is formalized as a problem of constructing the set of attainability for a control system generated by the Loewner equation. In this problem the maximum principle turns out to be a necessary and sufficient condition for optimality. An algorithm for finding this set for a generalized Loewner equation with constant coefficients and continuous control is constructed. The results are extended to classes of bounded univalent functions.","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":"126500705","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/SM1992V073N02ABEH002554
V. Roman’kov
The automorphism group of the free metabelian group is investigated. It is shown that has primitive elements not induced by primitive elements of . A criterion is provided for elements of to be primitive.
{"title":"PRIMITIVE ELEMENTS OF FREE GROUPS OF RANK 3","authors":"V. Roman’kov","doi":"10.1070/SM1992V073N02ABEH002554","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002554","url":null,"abstract":"The automorphism group of the free metabelian group is investigated. It is shown that has primitive elements not induced by primitive elements of . A criterion is provided for elements of to be primitive.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"22 4 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":"115823367","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/SM1992V073N02ABEH002557
A. Gonchar, N. Novikova, G. Khenkin
A study is made of approximate solutions of the inverse Sturm-Liouville problem, based on a construction of multipoint Pade approximants. Corresponding convergence theorems are proved.
{"title":"MULTIPOINT PADÉ APPROXIMANTS IN THE INVERSE STURM-LIOUVILLE PROBLEM","authors":"A. Gonchar, N. Novikova, G. Khenkin","doi":"10.1070/SM1992V073N02ABEH002557","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002557","url":null,"abstract":"A study is made of approximate solutions of the inverse Sturm-Liouville problem, based on a construction of multipoint Pade approximants. Corresponding convergence theorems are proved.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"25 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":"128952051","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/SM1992V071N01ABEH002128
V. Zhikov
For the diffusion equation in the exterior of a closed set , , with Neumann conditions on the boundary, 0,$ SRC=http://ej.iop.org/images/0025-5734/71/1/A09/tex_sm_2128_img3.gif/>??pointwise stabilization, the central limit theorem, and uniform stabilization are studied.The basic condition on the set is formulated in terms of extension properties. Model examples of sets are indicated which are of interest from the viewpoint of mathematical physics and applied probability theory.
{"title":"ASYMPTOTIC PROBLEMS CONNECTED WITH THE HEAT EQUATION IN PERFORATED DOMAINS","authors":"V. Zhikov","doi":"10.1070/SM1992V071N01ABEH002128","DOIUrl":"https://doi.org/10.1070/SM1992V071N01ABEH002128","url":null,"abstract":"For the diffusion equation in the exterior of a closed set , , with Neumann conditions on the boundary, 0,$ SRC=http://ej.iop.org/images/0025-5734/71/1/A09/tex_sm_2128_img3.gif/>??pointwise stabilization, the central limit theorem, and uniform stabilization are studied.The basic condition on the set is formulated in terms of extension properties. Model examples of sets are indicated which are of interest from the viewpoint of mathematical physics and applied probability theory.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"26 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":"129056483","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/SM1992V072N01ABEH001582
M. A. Babaev
The degree of best approximation by bilinear forms in Lp, where 1 ? q ? p ? 2, is established for the class Wqr.
双线性形式在Lp中的最佳近似度，其中1 ?问吗?p ?2、为类Wqr建立。
{"title":"ON THE DEGREE OF APPROXIMATION OF THE SOBOLEV CLASS Wqr BY BILINEAR FORMS IN Lp FOR 1 ? q ? p ? 2","authors":"M. A. Babaev","doi":"10.1070/SM1992V072N01ABEH001582","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001582","url":null,"abstract":"The degree of best approximation by bilinear forms in Lp, where 1 ? q ? p ? 2, is established for the class Wqr.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"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":"127749079","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/SM1992V073N02ABEH002548
V. Goncharov, A. Tolstonogov
A continuous version of a theorem of Lyapunov on convexity for measures with values in a Banach space is proved, and then used to obtain two results on the existence of a common continuous selection of finitely many multivalued mappings with values in a space of Bochner-integrable functions. These results are applied to the investigation of properties of solutions of differential inclusions with -accretive operators.
{"title":"Joint Continuous Selections of Multivalued Mappings with Nonconvex Values, and Their Applications","authors":"V. Goncharov, A. Tolstonogov","doi":"10.1070/SM1992V073N02ABEH002548","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002548","url":null,"abstract":"A continuous version of a theorem of Lyapunov on convexity for measures with values in a Banach space is proved, and then used to obtain two results on the existence of a common continuous selection of finitely many multivalued mappings with values in a space of Bochner-integrable functions. These results are applied to the investigation of properties of solutions of differential inclusions with -accretive operators.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"7 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":"117091845","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}
{"title":"ON THE CONNECTION BETWEEN MEAN OSCILLATION AND EXACT INTEGRABILITY CLASSES OF FUNCTIONS","authors":"A. Korenovskii","doi":"10.1070/SM1992V071N02ABEH001409","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001409","url":null,"abstract":"Exact integrability classes are obtained for the functions in the John-Nirenberg and Gurov-Reshetnyak inequalities.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"45 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":"122747336","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：