Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N02ABEH002133
S. T. Tulyaganov
We consider the following conjecture, which was made in 1970 by B. V. Levin and A. S. Faĭnleĭb; if , , , and (2) is fulfilled with , then (1) holds. We prove that this conjecture holds if . In the case we construct a counterexample to the conjecture. The asymptotic behavior of the sum of values of the function is found by an analytic method.
{"title":"ON A CONJECTURE ON SUMS OF MULTIPLICATIVE FUNCTIONS","authors":"S. T. Tulyaganov","doi":"10.1070/SM1992V071N02ABEH002133","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH002133","url":null,"abstract":"We consider the following conjecture, which was made in 1970 by B. V. Levin and A. S. Faĭnleĭb; if , , , and (2) is fulfilled with , then (1) holds. We prove that this conjecture holds if . In the case we construct a counterexample to the conjecture. The asymptotic behavior of the sum of values of the function is found by an analytic method.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"38 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":"123379290","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/SM1992V072N01ABEH001412
Y. Kuperin, Y. Melnikov
A geometric approach to the method of adiabatic representations is developed for a class of relativistic Hamiltonians. The theory is used to analyze the associated dynamical equations with effective nonabelian interactions that can be regarded as gauge fields, induced by dimensional reduction of the initial problem in a special representation. It is shown that the approach can be used to study 2?(2,?3) quantum scattering processes in a three-body system, and a one-to-one relation between the complete and the effective S-matrices is derived. Asymptotic expressions are found for the solutions of the effective dynamical equation and for the gauge fields in the adiabatic representations. The method is illustrated for systems admitting adiabatic representations with a one-dimensional base; in several cases the field operator is proved to be Hilbert-Schmidt.
{"title":"QUANTUM SCATTERING IN GAUGE FIELDS OF ADIABATIC REPRESENTATIONS","authors":"Y. Kuperin, Y. Melnikov","doi":"10.1070/SM1992V072N01ABEH001412","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001412","url":null,"abstract":"A geometric approach to the method of adiabatic representations is developed for a class of relativistic Hamiltonians. The theory is used to analyze the associated dynamical equations with effective nonabelian interactions that can be regarded as gauge fields, induced by dimensional reduction of the initial problem in a special representation. It is shown that the approach can be used to study 2?(2,?3) quantum scattering processes in a three-body system, and a one-to-one relation between the complete and the effective S-matrices is derived. Asymptotic expressions are found for the solutions of the effective dynamical equation and for the gauge fields in the adiabatic representations. The method is illustrated for systems admitting adiabatic representations with a one-dimensional base; in several cases the field operator is proved to be Hilbert-Schmidt.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"377 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":"116469027","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/SM1992V072N02ABEH001415
L. Bagirov, V. Kondrat'ev
Solutions of differential equations of first and arbitrary order in Hilbert space are investigated; they arise in the study of elliptic problems in cylindrical domains and in domains with singular points. Existence theorems are obtained for a broad class of right sides, and the asymptotics of a solution as t?∞ is constructed under "minimal" conditions on the coefficients. The results make considerable progress possible in the study of qualitative properties of solutions of elliptic equations of higher order.
{"title":"On the Asymptotics of Solutions of Differential Equations in Hilbert Space","authors":"L. Bagirov, V. Kondrat'ev","doi":"10.1070/SM1992V072N02ABEH001415","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH001415","url":null,"abstract":"Solutions of differential equations of first and arbitrary order in Hilbert space are investigated; they arise in the study of elliptic problems in cylindrical domains and in domains with singular points. Existence theorems are obtained for a broad class of right sides, and the asymptotics of a solution as t?∞ is constructed under \"minimal\" conditions on the coefficients. The results make considerable progress possible in the study of qualitative properties of solutions of elliptic equations of higher order.","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":"132838068","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/SM1992V073N02ABEH002558
K. N. Ponomarev
A study is made of the structure of minimal algebraic groups and their groups of points. As application, a description of the abstract isomorphisms of minimal groups is obtained.
研究了极小代数群及其点群的结构。作为应用，给出了最小群的抽象同构的描述。
{"title":"MINIMAL SOLVABLE ALGEBRAIC GROUPS AND THEIR ABSTRACT ISOMORPHISMS","authors":"K. N. Ponomarev","doi":"10.1070/SM1992V073N02ABEH002558","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002558","url":null,"abstract":"A study is made of the structure of minimal algebraic groups and their groups of points. As application, a description of the abstract isomorphisms of minimal groups is obtained.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"73 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":"130991370","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/SM1992V071N01ABEH002129
P. V. Paramonov
A criterion is established for the possibility of approximation by harmonic functions and, in particular, by harmonic polynomials in the -norm on compact subsets of . This criterion, which is in terms of harmonic -capacity in , yields a natural analog to the theorem of Vitushkin on rational approximation in terms of analytic capacity.
{"title":"ON HARMONIC APPROXIMATION IN THE $ C^1$-NORM","authors":"P. V. Paramonov","doi":"10.1070/SM1992V071N01ABEH002129","DOIUrl":"https://doi.org/10.1070/SM1992V071N01ABEH002129","url":null,"abstract":"A criterion is established for the possibility of approximation by harmonic functions and, in particular, by harmonic polynomials in the -norm on compact subsets of . This criterion, which is in terms of harmonic -capacity in , yields a natural analog to the theorem of Vitushkin on rational approximation in terms of analytic capacity.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"71 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":"131016894","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/SM1992V071N02ABEH002131
A. Sakhnovich
The author describes a set of pseudospectral functions of the canonical system of differential equations where In terms of the Hamiltonians , conditions are given under which the pseudospectral functions are spectral functions.
本文描述了正则微分方程组的一组伪谱函数，用哈密顿量给出了伪谱函数为谱函数的条件。
{"title":"SPECTRAL FUNCTIONS OF A CANONICAL SYSTEM OF ORDER $ 2n$","authors":"A. Sakhnovich","doi":"10.1070/SM1992V071N02ABEH002131","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH002131","url":null,"abstract":"The author describes a set of pseudospectral functions of the canonical system of differential equations where In terms of the Hamiltonians , conditions are given under which the pseudospectral functions are spectral functions.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"32 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":"132630351","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/SM1992V071N02ABEH001398
A. Bulgakov
It is proved that in the space of Bochner-integrable mappings a multivalued mapping with nonconvex images has a continuous branch that, for a given single-valued mapping and for a previously specified accuracy, realizes the distance between the images of the single-valued mapping and the multivalued mapping. This result is applied to the investigation of properties of solutions of functional-differential inclusions with nonconvex right-hand side.
{"title":"CONTINUOUS BRANCHES OF MULTIVALUED MAPPINGS AND FUNCTIONAL-DIFFERENTIAL INCLUSIONS WITH NONCONVEX RIGHT-HAND SIDE","authors":"A. Bulgakov","doi":"10.1070/SM1992V071N02ABEH001398","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001398","url":null,"abstract":"It is proved that in the space of Bochner-integrable mappings a multivalued mapping with nonconvex images has a continuous branch that, for a given single-valued mapping and for a previously specified accuracy, realizes the distance between the images of the single-valued mapping and the multivalued mapping. This result is applied to the investigation of properties of solutions of functional-differential inclusions with nonconvex right-hand side.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"32 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":"130112752","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/SM1992V072N01ABEH001267
V. Beloshapka
Holomorphic transformations of a quadric of arbitrary codimension are studied. General formulas are derived for infinitesimal automorphisms of such a surface. The phenomenon of "rigidity" of quadrics in general position is demonstrated. Examples of quadrics with rich automorphism groups are considered. A classification is given for positive-definite quadrics of codimension two.
{"title":"ON HOLOMORPHIC TRANSFORMATIONS OF A QUADRIC","authors":"V. Beloshapka","doi":"10.1070/SM1992V072N01ABEH001267","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001267","url":null,"abstract":"Holomorphic transformations of a quadric of arbitrary codimension are studied. General formulas are derived for infinitesimal automorphisms of such a surface. The phenomenon of \"rigidity\" of quadrics in general position is demonstrated. Examples of quadrics with rich automorphism groups are considered. A classification is given for positive-definite quadrics of codimension two.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"31 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":"125952525","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/SM1992V072N01ABEH002137
A. Agrachev, R. Gamkrelidze
With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory.
{"title":"SYMPLECTIC GEOMETRY AND NECESSARY CONDITIONS FOR OPTIMALITY","authors":"A. Agrachev, R. Gamkrelidze","doi":"10.1070/SM1992V072N01ABEH002137","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH002137","url":null,"abstract":"With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"18 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":"130426677","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/SM1992V073N01ABEH002539
A. Starkov
Horospherical flows are considered on homogeneous spaces of finite volume. An ergodic decomposition of such flows is constructed in explicit form, and it is proved that the horospherical orbits have constant dimension. A conjecture of Raghunathan is proved for the closure of the orbits of horospherical flows under the additional assumption that the homogeneous space is compact.
{"title":"HOROSPHERICAL FLOWS ON HOMOGENEOUS SPACES OF FINITE VOLUME","authors":"A. Starkov","doi":"10.1070/SM1992V073N01ABEH002539","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002539","url":null,"abstract":"Horospherical flows are considered on homogeneous spaces of finite volume. An ergodic decomposition of such flows is constructed in explicit form, and it is proved that the horospherical orbits have constant dimension. A conjecture of Raghunathan is proved for the closure of the orbits of horospherical flows under the additional assumption that the homogeneous space is compact.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"2016 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":"129024764","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：