Pub Date : 2014-11-05DOI: 10.1090/S0077-1554-2014-00234-X
STURM–LIOUVILLE Operators, K. A. Mirzoev
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{"title":"Sturm–Liouville operators","authors":"STURM–LIOUVILLE Operators, K. A. Mirzoev","doi":"10.1090/S0077-1554-2014-00234-X","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00234-X","url":null,"abstract":",","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00234-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627242","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 : 2014-11-05DOI: 10.1090/S0077-1554-2014-00235-1
M. M. Graev
This paper deals with the number of complex invariant Einstein metrics on flag spaces in the case when the isotropy representation has a simple spectrum. The author has previously showed that this number does not exceed the volume of the Newton polytope of the Einstein equation (in this case, this is a rational system of equations), which coincides with the Newton polytope of the scalar curvature function. The equality is attained precisely when that function has no singular points on the faces of the polytope, which is the case for “pyramidal faces”. This paper studies non-pyramidal faces. They are classified with the aid of ternary symmetric relations (which determine the Newton polytope) in the T -root system (the restriction of the root system of the Lie algebra of the group to the center of the isotropy subalgebra). The classification is mainly done by computer-assisted calculations for classical and exceptional groups in the case when the number of irreducible components does not exceed 10 (and, in some cases, 15).
{"title":"Einstein equations for invariant metrics on flag spaces and their Newton polytopes","authors":"M. M. Graev","doi":"10.1090/S0077-1554-2014-00235-1","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00235-1","url":null,"abstract":"This paper deals with the number of complex invariant Einstein metrics on flag spaces in the case when the isotropy representation has a simple spectrum. The author has previously showed that this number does not exceed the volume of the Newton polytope of the Einstein equation (in this case, this is a rational system of equations), which coincides with the Newton polytope of the scalar curvature function. The equality is attained precisely when that function has no singular points on the faces of the polytope, which is the case for “pyramidal faces”. This paper studies non-pyramidal faces. They are classified with the aid of ternary symmetric relations (which determine the Newton polytope) in the T -root system (the restriction of the root system of the Lie algebra of the group to the center of the isotropy subalgebra). The classification is mainly done by computer-assisted calculations for classical and exceptional groups in the case when the number of irreducible components does not exceed 10 (and, in some cases, 15).","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00235-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627256","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 : 2014-11-05DOI: 10.1090/S0077-1554-2014-00227-2
V. Ryzhikov
. We give some new examples of mixing transformations on a space with infinite measure: the so-called Sidon constructions of rank 1. We obtain rapid decay of correlations for a class of infinite transformations; this was recently discovered by Prikhod’ko for dynamical systems with simple spectrum acting on a probability space. We obtain an affirmative answer to Gordin’s question about the existence of transformations with zero entropy and an ergodic homoclinic flow. We consider mod-ifications of Sidon constructions inducing Poisson suspensions with simple singular spectrum and a homoclinic Bernoulli flow. We give a new proof of Roy’s theorem on multiple mixing of Poisson suspensions.
{"title":"Ergodic homoclinic groups, Sidon constructions and Poisson suspensions","authors":"V. Ryzhikov","doi":"10.1090/S0077-1554-2014-00227-2","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00227-2","url":null,"abstract":". We give some new examples of mixing transformations on a space with infinite measure: the so-called Sidon constructions of rank 1. We obtain rapid decay of correlations for a class of infinite transformations; this was recently discovered by Prikhod’ko for dynamical systems with simple spectrum acting on a probability space. We obtain an affirmative answer to Gordin’s question about the existence of transformations with zero entropy and an ergodic homoclinic flow. We consider mod-ifications of Sidon constructions inducing Poisson suspensions with simple singular spectrum and a homoclinic Bernoulli flow. We give a new proof of Roy’s theorem on multiple mixing of Poisson suspensions.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00227-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627566","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 : 2014-11-05DOI: 10.1090/S0077-1554-2014-00236-3
A. Domrin
. We establish that the Riemann problem on the factorization of formal matrix-valued Laurent series subject to unitary symmetry has a solution. As an application, we show that any local real-analytic solution (in x and t ) of the focusing nonlinear Schr¨odinger equation has a real-analytic extension to some strip parallel to the x -axis and that in each such strip there exists a solution that cannot be extended further.
{"title":"Real-analytic solutions of the nonlinear Schrödinger equation","authors":"A. Domrin","doi":"10.1090/S0077-1554-2014-00236-3","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00236-3","url":null,"abstract":". We establish that the Riemann problem on the factorization of formal matrix-valued Laurent series subject to unitary symmetry has a solution. As an application, we show that any local real-analytic solution (in x and t ) of the focusing nonlinear Schr¨odinger equation has a real-analytic extension to some strip parallel to the x -axis and that in each such strip there exists a solution that cannot be extended further.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00236-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627307","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 : 2014-11-04DOI: 10.1090/S0077-1554-2014-00226-0
K. Khachatryan
This paper is devoted to studying one class of nonlinear integral equations of Hammerstein–Nemytskĭı type on the whole axis, which occurs in the theory of transfer in inhomogeneous medium. It is proved that these equations can be solved in various function spaces, and the asymptotic behaviour at infinity of the solutions that are constructed is studied. §
{"title":"On positive solutions of one class of nonlinear integral equations of Hammerstein–Nemytskiĭ type on the whole axis","authors":"K. Khachatryan","doi":"10.1090/S0077-1554-2014-00226-0","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00226-0","url":null,"abstract":"This paper is devoted to studying one class of nonlinear integral equations of Hammerstein–Nemytskĭı type on the whole axis, which occurs in the theory of transfer in inhomogeneous medium. It is proved that these equations can be solved in various function spaces, and the asymptotic behaviour at infinity of the solutions that are constructed is studied. §","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00226-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627521","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 : 2014-11-04DOI: 10.1090/S0077-1554-2014-00229-6
V. Burenkov, M. Otelbaev
The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order 2l defined on a bounded domain in Rn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k 2l/n as k → ∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. §
{"title":"Comparison of the singular numbers of correct restrictions of elliptic differential operators","authors":"V. Burenkov, M. Otelbaev","doi":"10.1090/S0077-1554-2014-00229-6","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00229-6","url":null,"abstract":"The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order 2l defined on a bounded domain in Rn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k 2l/n as k → ∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. §","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00229-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627125","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 : 2014-11-04DOI: 10.1090/S0077-1554-2014-00228-4
V. Yurko
{"title":"Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges","authors":"V. Yurko","doi":"10.1090/S0077-1554-2014-00228-4","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00228-4","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00228-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627114","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 : 2014-04-28DOI: 10.1090/S0077-1554-07-00164-1
P. Gurevich, A. Skubachevskii
We consider elliptic equations of order $2m$ in a bounded domain $Qsubsetmathbb R^n$ with nonlocal boundary-value conditions connecting the values of a solution and its derivatives on $(n-1)$-dimensional smooth manifolds $Gamma_i$ with the values on manifolds $omega_{i}(Gamma_i)$, where $bigcup_ioverline{Gamma_i}=partial Q$ is a boundary of $Q$ and $omega_i$ are $C^infty$ diffeomorphisms. By proving a priori estimates for solutions and constructing a right regularizer, we show the Fredholm solvability in weighted space. For nonlocal elliptic problems with a parameter, we prove the unique solvability.
{"title":"On the Fredholm and unique solvability of nonlocal elliptic problems in multidimensional domains","authors":"P. Gurevich, A. Skubachevskii","doi":"10.1090/S0077-1554-07-00164-1","DOIUrl":"https://doi.org/10.1090/S0077-1554-07-00164-1","url":null,"abstract":"We consider elliptic equations of order $2m$ in a bounded domain $Qsubsetmathbb R^n$ with nonlocal boundary-value conditions connecting the values of a solution and its derivatives on $(n-1)$-dimensional smooth manifolds $Gamma_i$ with the values on manifolds $omega_{i}(Gamma_i)$, where $bigcup_ioverline{Gamma_i}=partial Q$ is a boundary of $Q$ and $omega_i$ are $C^infty$ diffeomorphisms. By proving a priori estimates for solutions and constructing a right regularizer, we show the Fredholm solvability in weighted space. For nonlocal elliptic problems with a parameter, we prove the unique solvability.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626122","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 : 2014-04-09DOI: 10.1090/S0077-1554-2014-00211-9
S. V. Shaposhnikov
{"title":"The Fokker–Planck–Kolmogorov equations with a potential and a non-uniformly elliptic diffusion matrix","authors":"S. V. Shaposhnikov","doi":"10.1090/S0077-1554-2014-00211-9","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00211-9","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00211-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626824","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 : 2014-04-09DOI: 10.1090/S0077-1554-2014-00224-7
A. Ayzenberg
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{"title":"Substitutions of polytopes and of simplicial complexes, and multigraded betti numbers","authors":"A. Ayzenberg","doi":"10.1090/S0077-1554-2014-00224-7","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00224-7","url":null,"abstract":",","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00224-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627508","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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