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Tunisian Journal of Mathematics最新文献

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On Poisson transforms for spinors 关于旋量的泊松变换
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2023-11-21 DOI: 10.2140/tunis.2023.5.771
S. Ben Saïd, A. Boussejra, K. Koufany
{"title":"On Poisson transforms for spinors","authors":"S. Ben Saïd, A. Boussejra, K. Koufany","doi":"10.2140/tunis.2023.5.771","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.771","url":null,"abstract":". Let ( τ, V τ ) be a spinor representation of Spin( n ) and let ( σ, V σ ) be a spinor representation of Spin( n − 1) that occurs in the restriction τ | Spin( n − 1) . We consider the real hyperbolic space H n ( R ) as the rank one homogeneous space Spin 0 (1 , n ) / Spin( n ) and the spinor bundle Σ H n ( R ) over H n ( R ) as the homogeneous bundle Spin 0 (1 , n ) × Spin( n ) V τ . Our aim is to characterize eigenspinors of the algebra of invariant differential operators acting on Σ H n ( R ) which can be written as the Poisson transform of L p -sections of the bundle Spin( n ) × Spin( n − 1) V σ over the boundary S n − 1 ≃ Spin( n ) / Spin( n − 1) of H n ( R ).","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"43 7","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139253017","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
An explicit formula for the Benjamin–Ono equation Benjamin-Ono方程的显式公式
Tunisian Journal of Mathematics Pub Date : 2023-11-02 DOI: 10.2140/tunis.2023.5.593
Patrick Gérard
{"title":"An explicit formula for the Benjamin–Ono equation","authors":"Patrick Gérard","doi":"10.2140/tunis.2023.5.593","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.593","url":null,"abstract":"We establish an explicit formula for the general solution of the Benjamin-Ono equation on the torus and on the line. Contents 1. Introduction 1 1.1. The Benjamin-Ono equation 1 1.2. The Lax pair 2 1.3. The explicit formula on the torus 3 1.4. The explicit formula on the line 3 1.5. Organization of the paper 4 2. Proof of the explicit formula on the torus 4 3. Proof of the explicit formula on the line 6 4. Final remarks 8 References 9","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"9 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934196","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: 10
Singularities of normal quartic surfaces, III : char = 2, nonsupersingular 正规四次曲面的奇异性，III: char = 2，非超奇异
Tunisian Journal of Mathematics Pub Date : 2023-11-02 DOI: 10.2140/tunis.2023.5.457
Fabrizio Catanese, Matthias Schütt
{"title":"Singularities of normal quartic surfaces, III : char = 2, nonsupersingular","authors":"Fabrizio Catanese, Matthias Schütt","doi":"10.2140/tunis.2023.5.457","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.457","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"31 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135973123","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
Nonlinear enhanced dissipation and inviscid damping for the 2D Couette flow 二维Couette流的非线性增强耗散和无粘阻尼
Tunisian Journal of Mathematics Pub Date : 2023-11-02 DOI: 10.2140/tunis.2023.5.573
Dongyi Wei, Zhifei Zhang
{"title":"Nonlinear enhanced dissipation and inviscid damping for the 2D Couette flow","authors":"Dongyi Wei, Zhifei Zhang","doi":"10.2140/tunis.2023.5.573","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.573","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"32 19","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135973268","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
The mod-p Riemann–Hilbert correspondenceand the perfect site 模-p Riemann-Hilbert对应关系与完全位置
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-05-23 DOI: 10.2140/tunis.2023.5.369
A. Mathew
{"title":"The mod-p Riemann–Hilbert correspondence\u0000and the perfect site","authors":"A. Mathew","doi":"10.2140/tunis.2023.5.369","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.369","url":null,"abstract":"The mod $p$ Riemann-Hilbert correspondence (in covariant and contravariant forms) relates $mathbb{F}_p$-'etale sheaves on the spectrum of an $mathbb{F}_p$-algebra $R$ and Frobenius modules over $R$. We give an exposition of these correspondences using Breen's vanishing results on the perfect site.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49268950","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
Asymptotics for the rotating fluids and primitive systems with large ill-prepared initial data in critical spaces 临界空间中初始数据不充分的旋转流体和原始系统的渐近性
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-04-12 DOI: 10.2140/tunis.2023.5.171
Frédéric Charve
{"title":"Asymptotics for the rotating fluids and primitive systems with large ill-prepared initial data in critical spaces","authors":"Frédéric Charve","doi":"10.2140/tunis.2023.5.171","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.171","url":null,"abstract":"In this article we study the lifespan and asymptotics (in the large rotation and stratification regime) for the Primitive system for highly ill-prepared initial data in critical spaces. Compared to our previous works, we simplified the proof and made it adaptable to the Rotating fluids system with highly ill-prepared initial data decomposed as a sum of 2D horizontal part and a very large 3D part. We also provide explicit convergence rates.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42178182","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
Quasi-2-Segal sets Quasi-2-Segal集
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-04-05 DOI: 10.2140/tunis.2023.5.327
M. Feller
{"title":"Quasi-2-Segal sets","authors":"M. Feller","doi":"10.2140/tunis.2023.5.327","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.327","url":null,"abstract":"We show that the 2-Segal spaces (also called decomposition spaces) of Dyckerhoff-Kapranov and G'alvez-Kock-Tonks have a natural analogue within simplicial sets, which we call quasi-2-Segal sets, and that the two ideas enjoy a similar relationship as the one Segal spaces have with quasi-categories. In particular, we construct a model structure on the category of simplicial sets whose fibrant objects are the quasi-2-Segal sets which is Quillen equivalent to a model structure for complete 2-Segal spaces (where our notion of completeness comes from one of the equivalent characterizations of completeness for Segal spaces). We also prove a path space criterion, which says that a simplicial set is a quasi-2-Segal set if and only if its path spaces (also called d'ecalage) are quasi-categories, as well as an edgewise subdivision criterion.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"58 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571915","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: 3
Uniformity of rational points: an up-date and corrections 有理点的一致性:更新和修正
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.183
L. Caporaso, J. Harris, B. Mazur
{"title":"Uniformity of rational points: an up-date and corrections","authors":"L. Caporaso, J. Harris, B. Mazur","doi":"10.2140/tunis.2022.4.183","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.183","url":null,"abstract":"In [2] it is asserted that, assuming the truth of the Strong Lang Conjecture (Conjecture 1 below), a very strong form of boundedness holds: for every g ≥ 2 there is a finite bound N(g)—not depending on K!—such that for any number field K there are only finitely many isomorphism classes of curves of genus g defined over K with more than N(g) K-rational points. The issue is, in that statement do we mean finitely many isomorphism classes over K, or over the algebraic closure K? The paper asserts the statement in the stronger form—up to isomorphism over K—but the proof establishes only the weaker statement that there are finitely many curves with more than N(g) points up to isomorphism over K.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68572262","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: 2
Constructibilité générique et uniformité enℓ 通用可建性和统一性,ℓ
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.159
L. Illusie
{"title":"Constructibilité générique et uniformité en\u0000ℓ","authors":"L. Illusie","doi":"10.2140/tunis.2022.4.159","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.159","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44974532","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
Uniform observation of semiclassicalSchrödinger eigenfunctions on an interval 区间上半经典薛定谔本征函数的一致观测
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-03-07 DOI: 10.2140/tunis.2023.5.125
Camille Laurent, Matthieu Léautaud
{"title":"Uniform observation of semiclassical\u0000Schrödinger eigenfunctions on an interval","authors":"Camille Laurent, Matthieu Léautaud","doi":"10.2140/tunis.2023.5.125","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.125","url":null,"abstract":"We consider eigenfunctions of a semiclassical Schr{\"o}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform in both semiclassical and high energy limits. These bounds are optimal and are used in an essential way in a companion paper in application to a controllability problem. The proofs rely on Agmon estimates and a Gronwall type argument in the classically forbidden region, and on the description of semiclassical measures for boundary value problems in the classically allowed region. Limited regularity for the potential is assumed.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41339095","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
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