Pub Date : 2023-11-21DOI: 10.2140/tunis.2023.5.771
S. Ben Saïd, A. Boussejra, K. Koufany
. 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 ).
.设 ( τ, V τ ) 为 Spin( n ) 的一个旋量表示，设 ( σ, V σ ) 为 Spin( n - 1) 的一个旋量表示，该表示出现在限制 τ | Spin( n - 1) 中。我们认为实双曲空间 H n ( R ) 是秩一均相空间 Spin 0 (1 , n ) / Spin( n ) ，而 H n ( R ) 上的旋光束 Σ H n ( R ) 是均相束 Spin 0 (1 , n ) × Spin( n ) V τ 。我们的目的是描述作用于 Σ H n ( R ) 的不变二阶算子代数的特征特征旋子，这些特征旋子可以写成 H n ( R ) 边界 S n - 1 ≃ Spin( n ) / Spin( n - 1) 上的 Spin( n ) × Spin( n - 1) V σ 束 L p 截面的泊松变换。
{"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":null,"pages":null},"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}
Pub Date : 2023-11-02DOI: 10.2140/tunis.2023.5.505
Yvan Martel, Ivan Naumkin
{"title":"Nonflat conformal blow-up profiles for the 1-dimensional critical nonlinear Schrödinger equation","authors":"Yvan Martel, Ivan Naumkin","doi":"10.2140/tunis.2023.5.505","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.505","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135973543","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 : 2023-11-02DOI: 10.2140/tunis.2023.5.593
Patrick Gérard
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
{"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":null,"pages":null},"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}
Pub Date : 2023-11-02DOI: 10.2140/tunis.2023.5.479
Scott Balchin, Ethan MacBrough, Kyle Ormsby
We isolate a class of groups -- called lossless groups -- for which homotopy classes of $G$-$N_infty$ operads are in bijection with certain restricted transfer systems on the poset of conjugacy classes $operatorname{Sub}(G)/G$.
{"title":"Lifting N∞ operads from conjugacy data","authors":"Scott Balchin, Ethan MacBrough, Kyle Ormsby","doi":"10.2140/tunis.2023.5.479","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.479","url":null,"abstract":"We isolate a class of groups -- called lossless groups -- for which homotopy classes of $G$-$N_infty$ operads are in bijection with certain restricted transfer systems on the poset of conjugacy classes $operatorname{Sub}(G)/G$.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934194","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 : 2023-11-02DOI: 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":null,"pages":null},"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}
Pub Date : 2023-11-02DOI: 10.2140/tunis.2023.5.405
Michel Gros, Bernard Le Stum, Adolfo Quirós
We show that the abstract equivalence of categories, called Cartier transform, between crystals on the q-crystalline and prismatic sites can be locally identified with the explicit local q-twisted Simpson correspondence. This establishes four equivalences that are all compatible with the relevant cohomology theories. We restrict ourselves for simplicity to the dimension one situation.
{"title":"Cartier transform and prismatic crystals","authors":"Michel Gros, Bernard Le Stum, Adolfo Quirós","doi":"10.2140/tunis.2023.5.405","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.405","url":null,"abstract":"We show that the abstract equivalence of categories, called Cartier transform, between crystals on the q-crystalline and prismatic sites can be locally identified with the explicit local q-twisted Simpson correspondence. This establishes four equivalences that are all compatible with the relevant cohomology theories. We restrict ourselves for simplicity to the dimension one situation.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135874771","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 : 2023-11-02DOI: 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":null,"pages":null},"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}
Pub Date : 2022-12-31DOI: 10.2140/tunis.2022.4.755
Hassan Mohsen, Simon Labrunie, Victor Nistor
{"title":"Estimations polynomiales pour les problèmes de transmission sur des domaines à bords plats","authors":"Hassan Mohsen, Simon Labrunie, Victor Nistor","doi":"10.2140/tunis.2022.4.755","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.755","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47862993","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 : 2022-08-24DOI: 10.2140/tunis.2022.4.329
Jean-Marc Delort
We prove a microlocal partition of energy for solutions to linear half-wave or Schrödinger equations in any space dimension. This extends well-known (local) results valid for the wave equation outside the wave cone, and allows us in particular, in the case of even dimension, to generalize the radial estimates due to Côte, Kenig and Schlag to non radial initial data. 0 Introduction The goal of this paper is to revisit the property of space partition of energy when time goes to infinity for solutions of linear wave equations that has been uncovered by Duyckaerts, Kenig and Merle [6, 7] in odd dimensions and by Côte, Kenig and Schlag [4] in even dimensions, and to extend it to other dispersive equations. Recall that if w solves the linear wave equation on R× Rd (∂ t −∆x)w = 0 w|t=0 = w0 ∂tw|t=0 = w1 and if one defines the energy at time t outside the wave cone by (1) E(w0, w1, t) = ∫ |x|>|t| [ |∂tw(t, x)| + |∇xw(t, x)| ] dx, then it has been proved in [6, 7] that, if d is odd, either ∀t ≥ 0, E(w0, w1, t) ≥ 1 2 [ ‖w1‖L2 + ‖∇xw0‖ 2 L2 ] or ∀t ≤ 0, E(w0, w1, t) ≥ 1 2 [ ‖w1‖L2 + ‖∇xw0‖ 2 L2 ] . (2) 2020 Mathematics Subject Classification: 35L05, 35Q41.
我们证明了在任何空间维度上线性半波或薛定谔方程解的能量的微局部分配。这扩展了对波锥外波动方程有效的已知（局部）结果，并特别允许我们在偶数维的情况下，将Côte、Kenig和Schlag的径向估计推广到非径向初始数据。0引言本文的目标是重新审视Duyckaerts、Kenig和Merle[6，7]在奇维和Côte、Kenig、Schlag[4]在偶维中发现的线性波动方程解在时间无穷大时能量的空间分配性质，并将其扩展到其他色散方程。回想一下，如果w求解R×Rd上的线性波动方程（⏴t-∆x）w=0 w | t=0=w0⏴[|w1 |L2+|xw0 |L2]或∀t≤0，E（w0，w1，t。（2） 2020数学学科分类：35L05、35Q41。
{"title":"Microlocal partition of energy for linear wave or\u0000Schrödinger equations","authors":"Jean-Marc Delort","doi":"10.2140/tunis.2022.4.329","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.329","url":null,"abstract":"We prove a microlocal partition of energy for solutions to linear half-wave or Schrödinger equations in any space dimension. This extends well-known (local) results valid for the wave equation outside the wave cone, and allows us in particular, in the case of even dimension, to generalize the radial estimates due to Côte, Kenig and Schlag to non radial initial data. 0 Introduction The goal of this paper is to revisit the property of space partition of energy when time goes to infinity for solutions of linear wave equations that has been uncovered by Duyckaerts, Kenig and Merle [6, 7] in odd dimensions and by Côte, Kenig and Schlag [4] in even dimensions, and to extend it to other dispersive equations. Recall that if w solves the linear wave equation on R× Rd (∂ t −∆x)w = 0 w|t=0 = w0 ∂tw|t=0 = w1 and if one defines the energy at time t outside the wave cone by (1) E(w0, w1, t) = ∫ |x|>|t| [ |∂tw(t, x)| + |∇xw(t, x)| ] dx, then it has been proved in [6, 7] that, if d is odd, either ∀t ≥ 0, E(w0, w1, t) ≥ 1 2 [ ‖w1‖L2 + ‖∇xw0‖ 2 L2 ] or ∀t ≤ 0, E(w0, w1, t) ≥ 1 2 [ ‖w1‖L2 + ‖∇xw0‖ 2 L2 ] . (2) 2020 Mathematics Subject Classification: 35L05, 35Q41.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49223404","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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