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Description explicite de la frontière de Poisson pour certains groupes de Lie résolubles connexes 某些相关可解李群的泊松边界的显式描述
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02121-8
Christophe Cuny
{"title":"Description explicite de la frontière de Poisson pour certains groupes de Lie résolubles connexes","authors":"Christophe Cuny","doi":"10.1016/S0764-4442(01)02121-8","DOIUrl":"10.1016/S0764-4442(01)02121-8","url":null,"abstract":"<div><p>Let <em>G</em> be a connected solvable Lie group with abelian derived group and <em>μ</em> be a spread out probability measure on <em>G</em>. We give an explicit description of the Poisson boundary in terms of almost sure convergence of the right random walk of law <em>μ</em>. We characterize the Poisson boundary by an integral criterion for some matricial groups.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 741-744"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02121-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80531866","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}
引用次数: 1
Spectre singulier pour les générateurs des semi-groupes 半群发电机的奇异谱
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02021-3
Abdelkader Elkoutri, Mohamed Aziz Taoudi
{"title":"Spectre singulier pour les générateurs des semi-groupes","authors":"Abdelkader Elkoutri,&nbsp;Mohamed Aziz Taoudi","doi":"10.1016/S0764-4442(01)02021-3","DOIUrl":"10.1016/S0764-4442(01)02021-3","url":null,"abstract":"<div><p>In this Note, we give necessary and sufficient conditions for the generator of a <span><math><mtext>C</mtext><msub><mi></mi><mn>0</mn></msub></math></span> semigroup to be semiregular. We also prove that the spectral inclusion for semigroups holds for the singular spectrum. By applying the preceding results, we establish some stability results for semigroups.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 641-644"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02021-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72778743","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}
引用次数: 7
Une généralisation du développement de Karhunen–Loève du pont brownien 推广Karhunen - loeve du pont brownien的发展
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02053-5
Jean-Renaud Pycke
{"title":"Une généralisation du développement de Karhunen–Loève du pont brownien","authors":"Jean-Renaud Pycke","doi":"10.1016/S0764-4442(01)02053-5","DOIUrl":"10.1016/S0764-4442(01)02053-5","url":null,"abstract":"<div><p>In this paper we give the Karhunen–Loève expansion of a centered Gaussian process whose covariance function depends on two parameters, including the covariance function of the Brownian bridge as a special case. A statistical application, related to the weighted uniform empirical process is provided.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 685-688"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02053-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78646719","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}
引用次数: 6
Résolution d'ambiguı̈tés entières sur graphes interférométriques et GPS 决议/过境ı̈次序一个个图表上的干涉和GPS
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02125-5
André Lannes
{"title":"Résolution d'ambiguı̈tés entières sur graphes interférométriques et GPS","authors":"André Lannes","doi":"10.1016/S0764-4442(01)02125-5","DOIUrl":"10.1016/S0764-4442(01)02125-5","url":null,"abstract":"<div><p>The notion of integer ambiguity resolution is associated with the problem of finding the point of<!--> <!--> <span><math><mtext>Z</mtext><msup><mi></mi><mn>n</mn></msup></math></span> closest to a point of<!--> <!--> <span><math><mtext>R</mtext><msup><mi></mi><mn>n</mn></msup></math></span>, the distance being the one induced by a given quadratic form. This problem is solved with the aid of computational techniques currently used in algebra of numbers. The notion of reduced basis then plays a key role. In interferometry (more precisely in phase closure imaging) and in GPS (Global positioning system), the statement of these problems also appeals to the notion of a graph, and thereby, to the related linear algebra. The corresponding approach, which is very attractive from a conceptual point of view, finally leads to very efficient solution methods.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 707-712"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02125-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73763424","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}
引用次数: 1
Sur la stricte concavité du rayon harmonique en dimension N⩾3 在N小于或等于3维的谐波半径的严格凹面上
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02126-7
Pierre Cardaliaguet , Rabah Tahraoui
{"title":"Sur la stricte concavité du rayon harmonique en dimension N⩾3","authors":"Pierre Cardaliaguet ,&nbsp;Rabah Tahraoui","doi":"10.1016/S0764-4442(01)02126-7","DOIUrl":"10.1016/S0764-4442(01)02126-7","url":null,"abstract":"<div><p>In this Note a result on the strict concavity of the harmonic radius in open convex domains of <span><math><mtext>R</mtext><msup><mi></mi><mn>N</mn></msup></math></span>, for <em>N</em>⩾3, is given. It implies the strict convexity of the Robin function and the uniqueness of the harmonic center in bounded convex domains.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 713-718"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02126-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84203124","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}
引用次数: 1
Un système dynamique lié à la suite des nombres premiers 与质数序列相连的动力系统
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02099-7
Alain Costé
{"title":"Un système dynamique lié à la suite des nombres premiers","authors":"Alain Costé","doi":"10.1016/S0764-4442(01)02099-7","DOIUrl":"10.1016/S0764-4442(01)02099-7","url":null,"abstract":"<div><p>We study the dynamical system defined by the map <span><math><mtext>Φ:</mtext><mspace></mspace><mtext>]0,1]→</mtext><mspace></mspace><mtext>]0,1]</mtext></math></span>, where <em>Φ</em>(<em>x</em>)=<em>px</em>−1 on ]1/<em>p</em>,1/<em>q</em>] if <em>q</em> and <em>p</em> are consecutive prime numbers. We relate the existence of an absolutely continuous invariant measure to ergodicity of a Markov chain <span><math><mtext>P</mtext></math></span> on the union of orbits stemming from numbers 1/<em>p</em> (<em>p</em> prime). We prove that ergodicity of <span><math><mtext>P</mtext></math></span> implies ergodicity of <em>Φ</em>. We establish a link between transfer probabilities of order <em>n</em> and some sets of sequences of the symbolic dynamic. This leads to a way of computing these coefficients using Monte Carlo method. We propose an algorithm which leads to a density indicating a good experimental fit with a typical orbit.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 663-668"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02099-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87577430","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}
引用次数: 0
A theorem on the strong asymptotic stability and determination of stabilizing controls 强渐近稳定性的一个定理及稳定控制的确定
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02129-2
Grigory Sklyar , Alexander Rezounenko
{"title":"A theorem on the strong asymptotic stability and determination of stabilizing controls","authors":"Grigory Sklyar ,&nbsp;Alexander Rezounenko","doi":"10.1016/S0764-4442(01)02129-2","DOIUrl":"10.1016/S0764-4442(01)02129-2","url":null,"abstract":"<div><p>In this work we show the role which plays a recent theorem on the strong asymptotic stability [17,14,1] in the analysis of the strong stabilizability problem in Hilbert spaces. We consider a control system with skew-adjoint operator and one-dimensional control. We examine in details the property for a linear feedback control to stabilize such a system. A robustness analysis of stabilizing controls is also given.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 807-812"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02129-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78555763","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}
引用次数: 9
Calcul pseudo-différentiel et équations d'évolution non linéaires sur les variétés compactes 紧流形上的伪微分计算和非线性演化方程
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02106-1
Mohammed Aassila
{"title":"Calcul pseudo-différentiel et équations d'évolution non linéaires sur les variétés compactes","authors":"Mohammed Aassila","doi":"10.1016/S0764-4442(01)02106-1","DOIUrl":"10.1016/S0764-4442(01)02106-1","url":null,"abstract":"<div><p>By using the pseudo-differential and para-differential calculus introduced by J.-M. Bony [1], we study the incompressible isotropic Navier–Stokes equations. We prove the short-time existence and uniqueness of solutions for arbitrary data with supercritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact Riemannian manifolds.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 617-622"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02106-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76620306","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}
引用次数: 4
Inequalities for the Gaussian measure and an application to Wiener space 高斯测度的不等式及其在维纳空间中的应用
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02122-X
Gilles Hargé
{"title":"Inequalities for the Gaussian measure and an application to Wiener space","authors":"Gilles Hargé","doi":"10.1016/S0764-4442(01)02122-X","DOIUrl":"10.1016/S0764-4442(01)02122-X","url":null,"abstract":"<div><p>This paper deals with a generalization of a result due to Brascamp and Lieb which states that in the space of probabilities with log-concave density with respect to a Gaussian measure on <span><math><mtext>R</mtext><msup><mi></mi><mn>n</mn></msup></math></span>, this Gaussian measure is the one which has strongest moments. We show that this theorem remains true if we replace <em>x</em><sup><em>α</em></sup> by a general convex function. Then, we deduce a correlation inequality for convex functions quite better than the one already known. Finally, we prove a result concerning stochastic analysis on Wiener space through the notion of approximate limit.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 791-794"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02122-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85672700","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}
引用次数: 6
Proof of Saffari's near-orthogonality conjecture for ultraflat sequences of unimodular polynomials 单模多项式超平坦序列的Saffari近正交猜想的证明
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02116-4
Tamás Erdélyi
{"title":"Proof of Saffari's near-orthogonality conjecture for ultraflat sequences of unimodular polynomials","authors":"Tamás Erdélyi","doi":"10.1016/S0764-4442(01)02116-4","DOIUrl":"10.1016/S0764-4442(01)02116-4","url":null,"abstract":"<div><p>Let <span><math><mtext>P</mtext><msub><mi></mi><mn>n</mn></msub><mtext>(z)=∑</mtext><msub><mi></mi><mn>k=0</mn></msub><msup><mi></mi><mn>n</mn></msup><mtext>a</mtext><msub><mi></mi><mn>k,n</mn></msub><mtext>z</mtext><msup><mi></mi><mn>k</mn></msup><mtext>∈</mtext><mtext>C</mtext><mspace></mspace><mtext>[z]</mtext></math></span> be a sequence of unimodular polynomials (|<em>a</em><sub><em>k</em>,<em>n</em></sub>|=1 for all <em>k</em>, <em>n</em>) which is ultraflat in the sense of Kahane, i.e., <span><span><span><math><mtext>lim</mtext><mtext>n→∞</mtext><mspace></mspace><mtext>max</mtext><mtext>|z|=1</mtext><mtext>|(n+1)</mtext><msup><mi></mi><mn>−1/2</mn></msup><mtext>|P</mtext><msub><mi></mi><mn>n</mn></msub><mtext>(z)|−1|=0.</mtext></math></span></span></span> We prove the following conjecture of Saffari (1991): ∑<sub><em>k</em>=0</sub><sup><em>n</em></sup><em>a</em><sub><em>k</em>,<em>n</em></sub><em>a</em><sub><em>n</em>−<em>k</em>,<em>n</em></sub>=o(<em>n</em>) as <em>n</em>→∞, that is, the polynomial <em>P</em><sub><em>n</em></sub>(<em>z</em>) and its “conjugate reciprocal” <span><math><mtext>P</mtext><msub><mi></mi><mn>n</mn></msub><msup><mi></mi><mn>∗</mn></msup><mtext>(z)=∑</mtext><msub><mi></mi><mn>k=0</mn></msub><msup><mi></mi><mn>n</mn></msup><mtext>a</mtext><msub><mi></mi><mn>n−k,n</mn></msub><mtext>z</mtext><msup><mi></mi><mn>k</mn></msup></math></span> become “nearly orthogonal” as <em>n</em>→∞. To this end we use results from [3] where (as well as in [5]) we studied the structure of ultraflat polynomials and proved several conjectures of Saffari.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 623-628"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02116-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75563596","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}
引用次数: 8
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