Some results related to Romanoff's theorem are obtained.
得到了一些与罗曼诺夫定理有关的结果。
{"title":"On Romanoff's theorem","authors":"A. Radomskii","doi":"10.4213/im9306e","DOIUrl":"https://doi.org/10.4213/im9306e","url":null,"abstract":"Some results related to Romanoff's theorem are obtained.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"1 8","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41249879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the standard conjecture for compactifications of Neron models of 4-dimensional Abelian varieties","authors":"S. G. Tankeev","doi":"10.1070/im9135","DOIUrl":"https://doi.org/10.1070/im9135","url":null,"abstract":"","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The intersection of two quadrics is called a biquadric. If we mark a non-singular quadric in the pencil of quadrics through a given biquadric, then the given biquadric is called a marked biquadric. In the classical papers of Plücker and Klein, a Kummer surface was canonically associated with every three-dimensional marked biquadric (that is, with a quadratic line complex provided that the Plücker–Klein quadric is marked). In Reid’s thesis, this correspondence was generalized to odd-dimensional marked biquadrics of arbitrary dimension . In this case, a Kummer variety of dimension corresponds to every biquadric of dimension . Reid only constructed the generalized Plücker–Klein correspondence. This map was not studied later. The present paper is devoted to a partial solution of the problem of creating the corresponding theory.
{"title":"The generalized Plücker–Klein map","authors":"V. A. Krasnov","doi":"10.1070/IM9073","DOIUrl":"https://doi.org/10.1070/IM9073","url":null,"abstract":"The intersection of two quadrics is called a biquadric. If we mark a non-singular quadric in the pencil of quadrics through a given biquadric, then the given biquadric is called a marked biquadric. In the classical papers of Plücker and Klein, a Kummer surface was canonically associated with every three-dimensional marked biquadric (that is, with a quadratic line complex provided that the Plücker–Klein quadric is marked). In Reid’s thesis, this correspondence was generalized to odd-dimensional marked biquadrics of arbitrary dimension . In this case, a Kummer variety of dimension corresponds to every biquadric of dimension . Reid only constructed the generalized Plücker–Klein correspondence. This map was not studied later. The present paper is devoted to a partial solution of the problem of creating the corresponding theory.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"25 1","pages":"291 - 333"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58575841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On solvability of second order semi-linear elliptic equations on closed manifolds","authors":"D. V. Tunitsky","doi":"10.1070/im9261","DOIUrl":"https://doi.org/10.1070/im9261","url":null,"abstract":"","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58577078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let be a finite group of Lie type and the Weyl group of . For every maximal torus of , we find the minimal order of a supplement of in its algebraic normalizer . In particular, we find all the maximal tori that have a complement in . Let correspond to an element of . We find the minimal orders of the lifts of the elements in .
{"title":"Minimal supplements of maximal tori in their normalizers for the groups","authors":"A. Galt, A. Staroletov","doi":"10.1070/IM9083","DOIUrl":"https://doi.org/10.1070/IM9083","url":null,"abstract":"Let be a finite group of Lie type and the Weyl group of . For every maximal torus of , we find the minimal order of a supplement of in its algebraic normalizer . In particular, we find all the maximal tori that have a complement in . Let correspond to an element of . We find the minimal orders of the lifts of the elements in .","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"86 1","pages":"126 - 149"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove necessary and (separate) sufficient conditions for the existence of unconditional bases of reproducing kernels in abstract radial Hilbert function spaces that are stable under division, in terms of the norms of monomials.
{"title":"Unconditional bases in radial Hilbert spaces","authors":"K. P. Isaev, R. S. Yulmukhametov","doi":"10.1070/IM9071","DOIUrl":"https://doi.org/10.1070/IM9071","url":null,"abstract":"We prove necessary and (separate) sufficient conditions for the existence of unconditional bases of reproducing kernels in abstract radial Hilbert function spaces that are stable under division, in terms of the norms of monomials.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"86 1","pages":"150 - 168"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On summable solutions of one class of nonlinear integral equations on the whole line","authors":"K. Khachatryan, H. S. Petrosyan","doi":"10.1070/im9211","DOIUrl":"https://doi.org/10.1070/im9211","url":null,"abstract":"","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Canonical representation of C*-algebra of eikonals related to the metric graph.","authors":"M. Belishev, Aleksandr Vladimirovich Kaplun","doi":"10.1070/im9179","DOIUrl":"https://doi.org/10.1070/im9179","url":null,"abstract":"","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58577207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We continue the work of improving the rate of convergence of ergodic homogeneous Markov chains. The setting is more general than in previous papers: we are able to get rid of the assumption about a common dominating measure and consider the case of inhomogeneous Markov chains as well as more general state spaces. We give examples where the new bound for the rate of convergence is the same as (resp. better than) the classical Markov–Dobrushin inequality.
{"title":"On improved bounds and conditions for the convergence of Markov chains","authors":"A. Veretennikov, M. Veretennikova","doi":"10.1070/IM9076","DOIUrl":"https://doi.org/10.1070/IM9076","url":null,"abstract":"We continue the work of improving the rate of convergence of ergodic homogeneous Markov chains. The setting is more general than in previous papers: we are able to get rid of the assumption about a common dominating measure and consider the case of inhomogeneous Markov chains as well as more general state spaces. We give examples where the new bound for the rate of convergence is the same as (resp. better than) the classical Markov–Dobrushin inequality.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"86 1","pages":"92 - 125"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study criteria for the finiteness of the constants in integral inequalities generalizing the Poincaré–Friedrichs inequality and Saint-Venant’s variational definition of torsional rigidity. The Rayleigh–Faber–Krahn isoperimetric inequality and the Saint-Venant–Pólya inequality guarantee the existence of finite constants for domains of finite volume. Criteria for the existence of finite constants for unbounded domains of infinite volume were known only in the cases of planar simply connected and spatial convex domains. We generalize and strengthen some known results and extend them to the case when . Here is one of our results. Suppose that and , where is a compact set and is either a planar domain with uniformly perfect boundary or a spatial domain satisfying the exterior sphere condition. Under these assumptions, a finite constant exists if and only if the integral is finite, where is the distance from the point to the boundary of .
{"title":"Embedding theorems related to torsional rigidity and principal frequency","authors":"F. Avkhadiev","doi":"10.1070/IM9085","DOIUrl":"https://doi.org/10.1070/IM9085","url":null,"abstract":"We study criteria for the finiteness of the constants in integral inequalities generalizing the Poincaré–Friedrichs inequality and Saint-Venant’s variational definition of torsional rigidity. The Rayleigh–Faber–Krahn isoperimetric inequality and the Saint-Venant–Pólya inequality guarantee the existence of finite constants for domains of finite volume. Criteria for the existence of finite constants for unbounded domains of infinite volume were known only in the cases of planar simply connected and spatial convex domains. We generalize and strengthen some known results and extend them to the case when . Here is one of our results. Suppose that and , where is a compact set and is either a planar domain with uniformly perfect boundary or a spatial domain satisfying the exterior sphere condition. Under these assumptions, a finite constant exists if and only if the integral is finite, where is the distance from the point to the boundary of .","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"86 1","pages":"1 - 31"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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