Pub Date : 1993-02-28DOI: 10.1070/SM1993V074N02ABEH003349
I. F. Krasichkov-Ternovskii
The problem of spectral synthesis in a complex domain for a differential operator with symbol , is reduced to the problem of a local description of the closed submodules of a module (of entire functions of exponential type) over the ring of polynomials of the form , .
{"title":"SPECTRAL SYNTHESIS IN A COMPLEX DOMAIN FOR A DIFFERENTIAL OPERATOR WITH CONSTANT COEFFICIENTS. I: A DUALITY THEOREM","authors":"I. F. Krasichkov-Ternovskii","doi":"10.1070/SM1993V074N02ABEH003349","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003349","url":null,"abstract":"The problem of spectral synthesis in a complex domain for a differential operator with symbol , is reduced to the problem of a local description of the closed submodules of a module (of entire functions of exponential type) over the ring of polynomials of the form , .","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"4 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":"129228914","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/SM1993V074N02ABEH003354
A. Sukhov
{"title":"ON ALGEBRAICITY OF COMPLEX ANALYTIC SETS","authors":"A. Sukhov","doi":"10.1070/SM1993V074N02ABEH003354","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003354","url":null,"abstract":"","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"15 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":"127152819","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/SM1993V074N02ABEH003350
A. Tsikh
It is proved that the Taylor series of a meromorphic function of two variables converges absolutely in the closed unit bidisk if this function satisfies a Holder condition in with exponent , while for any there exists a rational function with Holder exponent such that the indicated series diverges. This result solves the problem of stability of two-dimensional recursive digital filters. In its proof the structure of the asymptotic behavior of the Taylor coefficients of a meromorphic function of two variables is investigated.
{"title":"CONDITIONS FOR ABSOLUTE CONVERGENCE OF THE TAYLOR COEFFICIENT SERIES OF A MEROMORPHIC FUNCTION OF TWO VARIABLES","authors":"A. Tsikh","doi":"10.1070/SM1993V074N02ABEH003350","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003350","url":null,"abstract":"It is proved that the Taylor series of a meromorphic function of two variables converges absolutely in the closed unit bidisk if this function satisfies a Holder condition in with exponent , while for any there exists a rational function with Holder exponent such that the indicated series diverges. This result solves the problem of stability of two-dimensional recursive digital filters. In its proof the structure of the asymptotic behavior of the Taylor coefficients of a meromorphic function of two variables is investigated.","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":"124119891","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/SM1993V074N02ABEH003355
A. Babin
The Navier-Stokes system is considered in a plane domain that has several exits to infinity having the form of channels of bounded width. It is assumed that the external force decays sufficiently fast at infinity. Solutions are considered that are defined and bounded for all . Such solutions lie on an attractor of the system. An asymptotic expansion as is obtained for these solutions. The presence of this expansion indicates, in particular, that turbulence in this situation does not propagate to infinity.
{"title":"ASYMPTOTICS AS $ vert xverttoinfty$ OF FUNCTIONS LYING ON AN ATTRACTOR OF THE TWO-DIMENSIONAL NAVIER-STOKES SYSTEM IN AN UNBOUNDED PLANE DOMAIN","authors":"A. Babin","doi":"10.1070/SM1993V074N02ABEH003355","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003355","url":null,"abstract":"The Navier-Stokes system is considered in a plane domain that has several exits to infinity having the form of channels of bounded width. It is assumed that the external force decays sufficiently fast at infinity. Solutions are considered that are defined and bounded for all . Such solutions lie on an attractor of the system. An asymptotic expansion as is obtained for these solutions. The presence of this expansion indicates, in particular, that turbulence in this situation does not propagate to infinity.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"15 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":"122256858","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/SM1993V074N01ABEH003331
M. Zarichnyǐ
An investigation is made of the geometry of the multiplication mappings for monads whose functorial parts are (weakly) normal (in the sense of Shchepin) functors acting in the category of compacta. A characterization is obtained for a power monad as the only normal monad such that the multiplication mapping is soft for some omega_1$ SRC=http://ej.iop.org/images/0025-5734/74/1/A02/tex_sm_3331_img4.gif/>. It is proved that the multiplication mappings and of the inclusion hyperspace monad and the monad of complete chained systems are homeomorphic to trivial Tychonoff fibrations for openly generated continua that are homogeneous with respect to character.
{"title":"ABSOLUTE EXTENSORS AND THE GEOMETRY OF MULTIPLICATION OF MONADS IN THE CATEGORY OF COMPACTA","authors":"M. Zarichnyǐ","doi":"10.1070/SM1993V074N01ABEH003331","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003331","url":null,"abstract":"An investigation is made of the geometry of the multiplication mappings for monads whose functorial parts are (weakly) normal (in the sense of Shchepin) functors acting in the category of compacta. A characterization is obtained for a power monad as the only normal monad such that the multiplication mapping is soft for some omega_1$ SRC=http://ej.iop.org/images/0025-5734/74/1/A02/tex_sm_3331_img4.gif/>. It is proved that the multiplication mappings and of the inclusion hyperspace monad and the monad of complete chained systems are homeomorphic to trivial Tychonoff fibrations for openly generated continua that are homogeneous with respect to character.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"10 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":"134033262","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/SM1993V074N01ABEH003334
A. S. Loginov
A refinement is given for a result of M. S. Bazelkov on the exact constant of interpolation of the class of continuous functions with a given convex majorant of the modulus of continuity by Bernstein polynomials.
本文利用Bernstein多项式，对M. S. Bazelkov关于一类具有给定连续模凸主量的连续函数的精确插值常数的结果进行了改进。
{"title":"INTERPOLATION OF CONTINUOUS FUNCTIONS BY BERNSTEIN POLYNOMIALS ON TRIANGULABLE DOMAINS","authors":"A. S. Loginov","doi":"10.1070/SM1993V074N01ABEH003334","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003334","url":null,"abstract":"A refinement is given for a result of M. S. Bazelkov on the exact constant of interpolation of the class of continuous functions with a given convex majorant of the modulus of continuity by Bernstein polynomials.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"96 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":"132401552","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/SM1993V074N02ABEH003357
A. A. Il’in
Steady-state and time-dependent problems are studied for the equation where , is a two-dimensional closed manifold, and is the projection onto the subspace of solenoidal vector fields that admit a single-valued flow function. Existence of steady-state solutions is proved. For the evolution problem Lyapunov stability of the zero solution in Sobolev-Liouville spaces is proved by the method of vanishing viscosity. The existence of generalized weak attractors, an integer, is proved. A -weak attractor is constructed in the phase space for the velocity vortex equation.
{"title":"THE EULER EQUATIONS WITH DISSIPATION","authors":"A. A. Il’in","doi":"10.1070/SM1993V074N02ABEH003357","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003357","url":null,"abstract":"Steady-state and time-dependent problems are studied for the equation where , is a two-dimensional closed manifold, and is the projection onto the subspace of solenoidal vector fields that admit a single-valued flow function. Existence of steady-state solutions is proved. For the evolution problem Lyapunov stability of the zero solution in Sobolev-Liouville spaces is proved by the method of vanishing viscosity. The existence of generalized weak attractors, an integer, is proved. A -weak attractor is constructed in the phase space for the velocity vortex equation.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"15 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":"133624899","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/SM1993V074N01ABEH003343
M. Borsuk
Best-possible estimates are obtained for solutions of the Dirichlet problem for linear elliptic nondivergence equations of second order near a conical point of the boundary of the domain under minimal conditions on the smoothness of the coefficients of the equation.
{"title":"BEST-POSSIBLE ESTIMATES OF SOLUTIONS OF THE DIRICHLET PROBLEM FOR LINEAR ELLIPTIC NONDIVERGENCE EQUATIONS OF SECOND ORDER IN A NEIGHBORHOOD OF A CONICAL POINT OF THE BOUNDARY","authors":"M. Borsuk","doi":"10.1070/SM1993V074N01ABEH003343","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003343","url":null,"abstract":"Best-possible estimates are obtained for solutions of the Dirichlet problem for linear elliptic nondivergence equations of second order near a conical point of the boundary of the domain under minimal conditions on the smoothness of the coefficients of the equation.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"29 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":"122358522","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/SM1993V074N02ABEH003356
A. V. Lëtchikov
Random walks in a random environment are considered on the set of integers when the moving particle can go at most steps to the right and at most steps to the left in a unit of time. The transition probabilities for such a random walk from a point are determined by the vector . It is assumed that the sequence is a sequence of independent identically distributed random vectors. Asymptotic properties with probability 1 are investigated for such a random process. An invariance principle and the law of the iterated logarithm for a product of independent random matrices are proved as auxiliary results.
{"title":"ASYMPTOTIC PROPERTIES WITH PROBABILITY 1 FOR ONE-DIMENSIONAL RANDOM WALKS IN A RANDOM ENVIRONMENT","authors":"A. V. Lëtchikov","doi":"10.1070/SM1993V074N02ABEH003356","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003356","url":null,"abstract":"Random walks in a random environment are considered on the set of integers when the moving particle can go at most steps to the right and at most steps to the left in a unit of time. The transition probabilities for such a random walk from a point are determined by the vector . It is assumed that the sequence is a sequence of independent identically distributed random vectors. Asymptotic properties with probability 1 are investigated for such a random process. An invariance principle and the law of the iterated logarithm for a product of independent random matrices are proved as auxiliary results.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"59 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":"129650456","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/SM1993V074N02ABEH003363
M. N. Pantyukhina
It is shown that if a quasiconformal automorphism of the unit ball in () has coefficient of quasiconformality in the ball of radius with asymptotic growth such that , then it has a radial limit at almost every point of the boundary. This asymptotic growth of is sharp in a certain sense.
{"title":"ASYMPTOTICS OF THE COEFFICIENT OF QUASICONFORMALITY, AND THE BOUNDARY BEHAVIOR OF A MAPPING OF A BALL","authors":"M. N. Pantyukhina","doi":"10.1070/SM1993V074N02ABEH003363","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003363","url":null,"abstract":"It is shown that if a quasiconformal automorphism of the unit ball in () has coefficient of quasiconformality in the ball of radius with asymptotic growth such that , then it has a radial limit at almost every point of the boundary. This asymptotic growth of is sharp in a certain sense.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"41 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":"115151846","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：