Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N01ABEH002544
M. Sukhinin
Sufficient conditions for an extremum of second-order type are considered on the basis of the concepts (introduced in the paper) of -Taylor mappings and lower -semi-Taylor mappings, where is a norm in a linear space , and is a topology in a subset . Examples are given illustrating the novelty of the results obtained. Among the references devoted to sufficient conditions for an extremum, [1] (§3.4) and [2] (§6) should be mentioned.
{"title":"LOWER SEMI-TAYLOR MAPPINGS AND SUFFICIENT CONDITIONS FOR AN EXTREMUM","authors":"M. Sukhinin","doi":"10.1070/SM1992V073N01ABEH002544","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002544","url":null,"abstract":"Sufficient conditions for an extremum of second-order type are considered on the basis of the concepts (introduced in the paper) of -Taylor mappings and lower -semi-Taylor mappings, where is a norm in a linear space , and is a topology in a subset . Examples are given illustrating the novelty of the results obtained. Among the references devoted to sufficient conditions for an extremum, [1] (§3.4) and [2] (§6) should be mentioned.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"146 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":"126276298","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/SM1992V073N01ABEH002542
A. B. Shishkin
This paper is devoted to spectral synthesis of the operator adjoint to multiplication by a power of the independent variable in weighted spaces of entire functions of a single complex variable, and is closely connected with equations of convolution type, and with the general theory of subspaces invariant under a multiple differentiation operator. The problem of approximating solutions of a homogeneous equation of -sided convolution type by elementary solutions is solved. Certain systems of such equations are investigated.
{"title":"SPECTRAL SYNTHESIS FOR AN OPERATOR GENERATED BY MULTIPLICATION BY A POWER OF THE INDEPENDENT VARIABLE","authors":"A. B. Shishkin","doi":"10.1070/SM1992V073N01ABEH002542","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002542","url":null,"abstract":"This paper is devoted to spectral synthesis of the operator adjoint to multiplication by a power of the independent variable in weighted spaces of entire functions of a single complex variable, and is closely connected with equations of convolution type, and with the general theory of subspaces invariant under a multiple differentiation operator. The problem of approximating solutions of a homogeneous equation of -sided convolution type by elementary solutions is solved. Certain systems of such equations are investigated.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"11 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":"126087470","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/SM1992V072N01ABEH001262
A. A. Davydov
Structural stability of a smooth control system in general position on a smooth orientable compact surface is proved. This result is an analogue for control systems of the theorem on structural stability of a smooth vector field in general position on the sphere.
{"title":"STRUCTURAL STABILITY OF CONTROL SYSTEMS ON ORIENTABLE SURFACES","authors":"A. A. Davydov","doi":"10.1070/SM1992V072N01ABEH001262","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001262","url":null,"abstract":"Structural stability of a smooth control system in general position on a smooth orientable compact surface is proved. This result is an analogue for control systems of the theorem on structural stability of a smooth vector field in general position on the sphere.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"52 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":"116122718","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/SM1992V072N01ABEH001266
P. Zabreiko, V. I. Nazarov
Smoothness of solutions of ordinary differential equations of first and higher orders are considered in spaces of infinitely differentiable Roumieu functions. Various conditions on the right sides of the equations are studied for which smooth solutions of the equations lie in some Roumieu space.
{"title":"Smoothness Properties of Solutions of Nonlinear Differential Equations","authors":"P. Zabreiko, V. I. Nazarov","doi":"10.1070/SM1992V072N01ABEH001266","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001266","url":null,"abstract":"Smoothness of solutions of ordinary differential equations of first and higher orders are considered in spaces of infinitely differentiable Roumieu functions. Various conditions on the right sides of the equations are studied for which smooth solutions of the equations lie in some Roumieu space.","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":"130648097","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/SM1992V071N02ABEH001406
M. Fedoryuk
Necessary and sufficient conditions are obtained for a deformation to be isomonodromic for higher-order systems and equations in a neighborhood of an irregular singular point in the case when all formal solutions are subnormal series. Examples are considered.
{"title":"ISOMONODROMY DEFORMATIONS OF EQUATIONS WITH IRREGULAR SINGULARITIES","authors":"M. Fedoryuk","doi":"10.1070/SM1992V071N02ABEH001406","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001406","url":null,"abstract":"Necessary and sufficient conditions are obtained for a deformation to be isomonodromic for higher-order systems and equations in a neighborhood of an irregular singular point in the case when all formal solutions are subnormal series. Examples are considered.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"69 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":"131892990","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/SM1992V072N01ABEH001263
S. Agayan
For a commutative loc-Banach algebra over a complete valued field a structure sheaf is defined which coincides with the Zariski sheaf in the trivially valued case. As one consequence this gives a new way of constructing the holomorphic calculus.
{"title":"THE STRUCTURE SHEAF OF A BANACH ALGEBRA","authors":"S. Agayan","doi":"10.1070/SM1992V072N01ABEH001263","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001263","url":null,"abstract":"For a commutative loc-Banach algebra over a complete valued field a structure sheaf is defined which coincides with the Zariski sheaf in the trivially valued case. As one consequence this gives a new way of constructing the holomorphic calculus.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"6 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":"131041449","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/SM1992V073N01ABEH002537
K. Osipenko
The author considers problems of best recovery of a functional , , in the space of harmonic functions for or 2, in terms of the values of the functions and their derivatives at points of the interval . In the space the problem of constructing best quadrature formulas is solved. The existence of optimal quadrature formulas is proved, and, under certain conditions, the uniqueness of the optimal knots.
{"title":"BEST AND OPTIMAL RECOVERY METHODS FOR CLASSES OF HARMONIC FUNCTIONS","authors":"K. Osipenko","doi":"10.1070/SM1992V073N01ABEH002537","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002537","url":null,"abstract":"The author considers problems of best recovery of a functional , , in the space of harmonic functions for or 2, in terms of the values of the functions and their derivatives at points of the interval . In the space the problem of constructing best quadrature formulas is solved. The existence of optimal quadrature formulas is proved, and, under certain conditions, the uniqueness of the optimal knots.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"16 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":"121513042","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/SM1992V073N01ABEH002541
B. Khabibullin
Let and be subharmonic functions of finite order on . The main theorem of this paper shows that, if , the relation "" is preserved, in a certain sense, for mass distributions and . This result yields new uniqueness theorems for both subharmonic and entire functions on the complex plane.Corollaries include a broad class of sufficient conditions for the completeness of systems of exponential functions in a complex domain . The conditions for completeness are stated entirely in terms of the distribution of the points of the sequence in the neighborhood of infinity and in terms of the geometric properties (mixed areas) of .
{"title":"A UNIQUENESS THEOREM FOR SUBHARMONIC FUNCTIONS OF FINITE ORDER","authors":"B. Khabibullin","doi":"10.1070/SM1992V073N01ABEH002541","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002541","url":null,"abstract":"Let and be subharmonic functions of finite order on . The main theorem of this paper shows that, if , the relation \"\" is preserved, in a certain sense, for mass distributions and . This result yields new uniqueness theorems for both subharmonic and entire functions on the complex plane.Corollaries include a broad class of sufficient conditions for the completeness of systems of exponential functions in a complex domain . The conditions for completeness are stated entirely in terms of the distribution of the points of the sequence in the neighborhood of infinity and in terms of the geometric properties (mixed areas) of .","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"5 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":"122093466","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/SM1992V071N02ABEH001405
S. Khabirov
The equations of one-dimensional gas dynamics in Lagrange coordinates are connected with the inhomogeneous Monge-Ampere equation by means of a differential substitution. A classification of Monge-Ampere equations based on point and contact transformations is carried out. In the case of an infinite group various linearizations of the equations of gas dynamics are presented. New conservation laws are constructed on the basis of Noether's theorem. Examples of invariant solutions with variable entropy are considered, and some boundary value problems with curved shock waves are also solved.
{"title":"NONISENTROPIC ONE-DIMENSIONAL GAS MOTIONS CONSTRUCTED BY MEANS OF THE CONTACT GROUP OF THE NONHOMOGENEOUS MONGE-AMPÈRE EQUATION","authors":"S. Khabirov","doi":"10.1070/SM1992V071N02ABEH001405","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001405","url":null,"abstract":"The equations of one-dimensional gas dynamics in Lagrange coordinates are connected with the inhomogeneous Monge-Ampere equation by means of a differential substitution. A classification of Monge-Ampere equations based on point and contact transformations is carried out. In the case of an infinite group various linearizations of the equations of gas dynamics are presented. New conservation laws are constructed on the basis of Noether's theorem. Examples of invariant solutions with variable entropy are considered, and some boundary value problems with curved shock waves are also solved.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"126 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":"128055742","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/SM1992V071N02ABEH001403
I. F. Krasichkov-Ternovskii
A general approach is worked out for problems of complex analysis connected with the transition from local properties of analytic functions (of a single variable) to their global properties.
对于复杂分析问题，从解析函数(单变量)的局部性质到全局性质的转换，提出了一种一般的解决方法。
{"title":"ABSTRACT METHODS FOR A LOCAL DESCRIPTION OF CLOSED SUBMODULES OF ANALYTIC FUNCTIONS","authors":"I. F. Krasichkov-Ternovskii","doi":"10.1070/SM1992V071N02ABEH001403","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001403","url":null,"abstract":"A general approach is worked out for problems of complex analysis connected with the transition from local properties of analytic functions (of a single variable) to their global properties.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"12 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":"132920252","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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