{"title":"On a class of singular Sturm–Liouville problems","authors":"A. Vladimirov","doi":"10.1090/mosc/295","DOIUrl":"https://doi.org/10.1090/mosc/295","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"80 1","pages":"211-219"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45332746","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":"Ordinary differential operators and the integral representation of sums of certain power series","authors":"K. A. Mirzoev, T. Safonova","doi":"10.1090/mosc/294","DOIUrl":"https://doi.org/10.1090/mosc/294","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"80 1","pages":"133-151"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44721636","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":"Control with point observation for a parabolic problem with convection","authors":"I. Astashova, D. Lashin, A. V. Filinovskii","doi":"10.1090/mosc/296","DOIUrl":"https://doi.org/10.1090/mosc/296","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"80 1","pages":"221-234"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45937753","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 solvability of a class of nonlinear integral equations in the problem of a spread of an epidemic","authors":"A. Sergeev, K. Khachatryan","doi":"10.1090/mosc/286","DOIUrl":"https://doi.org/10.1090/mosc/286","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"80 1","pages":"95-111"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/mosc/286","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47813250","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":"Products of conjugacy classes in $mathrm {SL}_2(mathbb {R})$","authors":"S. Orevkov","doi":"10.1090/mosc/287","DOIUrl":"https://doi.org/10.1090/mosc/287","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"80 1","pages":"73-81"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/mosc/287","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48395813","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":"Homogenization over the spatial variable in nonlinear parabolic systems","authors":"S. Kashchenko","doi":"10.1090/mosc/288","DOIUrl":"https://doi.org/10.1090/mosc/288","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"80 1","pages":"53-71"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42983043","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}
The embedding constants of the Sobolev spaces $mathring{W}^n_2[0;1] hookrightarrow mathring{W}^k_infty[0; 1]$ ($0leqslant k leqslant n-1$) are studied. A relation of the embedding constants with the norms of the functionals $fmapsto f^{(k)}(a)$ in the space $mathring{W}^n_2[0;1]$ is given. An explicit form of the functions $g_{n;k}in mathring{W}^n_2[0;1]$ on which these functionals attain their norm is found. These functions are also to be extremal for the embedding constants. A relation of the embedding constants to the Legendre polynomials is put forward. A detailed study is made of the embedding constants with k = 3 and k = 5: we found explicit formulas for extreme points, calculate global maximum points, and give the values of the sharp embedding constants. A link between the embedding constants and some class of spectral problems with distribution coefficients is discovered.
{"title":"An explicit form for extremal functions in the embedding constant problem for Sobolev spaces","authors":"I. Sheipak, T. Garmanova","doi":"10.1090/mosc/292","DOIUrl":"https://doi.org/10.1090/mosc/292","url":null,"abstract":"The embedding constants of the Sobolev spaces $mathring{W}^n_2[0;1] hookrightarrow mathring{W}^k_infty[0; 1]$ ($0leqslant k leqslant n-1$) are studied. A relation of the embedding constants with the norms of the functionals $fmapsto f^{(k)}(a)$ in the space $mathring{W}^n_2[0;1]$ is given. An explicit form of the functions $g_{n;k}in mathring{W}^n_2[0;1]$ on which these functionals attain their norm is found. These functions are also to be extremal for the embedding constants. A relation of the embedding constants to the Legendre polynomials is put forward. A detailed study is made of the embedding constants with k = 3 and k = 5: we found explicit formulas for extreme points, calculate global maximum points, and give the values of the sharp embedding constants. A link between the embedding constants and some class of spectral problems with distribution coefficients is discovered.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48037288","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}
This work contains the following results: the trajectory fullness of the homoclinic groups, their connections with factors, K-property, weak multiple mixing; the ergodicity of the weakly homoclinic group for Gauss and Poisson actions; the triviality of the weakly homoclinic group for classes of rank-1 actions. Some open problems are discussed.
{"title":"Weakly homoclinic groups of ergodic actions","authors":"V. Ryzhikov","doi":"10.1090/mosc/289","DOIUrl":"https://doi.org/10.1090/mosc/289","url":null,"abstract":"This work contains the following results: the trajectory fullness of the homoclinic groups, their connections with factors, K-property, weak multiple mixing; the ergodicity of the weakly homoclinic group for Gauss and Poisson actions; the triviality of the weakly homoclinic group for classes of rank-1 actions. Some open problems are discussed.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49102661","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":"A modification of the Bloom–Graham Theorem: the introduction of weights in the complex tangent space","authors":"M. Stepanova","doi":"10.1090/MOSC/282","DOIUrl":"https://doi.org/10.1090/MOSC/282","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45148675","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":"Symmetric differential operators of fractional order and their extensions","authors":"N. Tokmagambetov, B. Torebek","doi":"10.1090/MOSC/279","DOIUrl":"https://doi.org/10.1090/MOSC/279","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/279","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45998024","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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