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On Poisson transforms for spinors 关于旋量的泊松变换
IF 0.9 Q2 MATHEMATICS Pub Date : 2023-11-21 DOI: 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。
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引用次数: 0
Nonflat conformal blow-up profiles for the 1-dimensional critical nonlinear Schrödinger equation 一维临界非线性Schrödinger方程的非平坦保形爆破剖面
Q2 MATHEMATICS Pub Date : 2023-11-02 DOI: 10.2140/tunis.2023.5.505
Yvan Martel, Ivan Naumkin
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引用次数: 0
An explicit formula for the Benjamin–Ono equation Benjamin-Ono方程的显式公式
Q2 MATHEMATICS Pub Date : 2023-11-02 DOI: 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
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引用次数: 10
Lifting N∞ operads from conjugacy data 从共轭数据中提升N∞操作
Q2 MATHEMATICS Pub Date : 2023-11-02 DOI: 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 $operatorname{Sub}(G)/G$.
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引用次数: 2
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
Q2 MATHEMATICS Pub Date : 2023-11-02 DOI: 10.2140/tunis.2023.5.457
Fabrizio Catanese, Matthias Schütt
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引用次数: 0
Cartier transform and prismatic crystals 卡地亚变换晶体和棱镜晶体
Q2 MATHEMATICS Pub Date : 2023-11-02 DOI: 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.
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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
Q2 MATHEMATICS Pub Date : 2023-11-02 DOI: 10.2140/tunis.2023.5.573
Dongyi Wei, Zhifei Zhang
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引用次数: 1
Estimations polynomiales pour les problèmes de transmission sur des domaines à bords plats 平边域上传输问题的多项式估计
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-12-31 DOI: 10.2140/tunis.2022.4.755
Hassan Mohsen, Simon Labrunie, Victor Nistor
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引用次数: 1
Microlocal partition of energy for linear wave orSchrödinger equations 线性波或Schrödinger方程能量的微局部分配
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-08-24 DOI: 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。
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引用次数: 4
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 Q2 MATHEMATICS Pub Date : 2022-05-23 DOI: 10.2140/tunis.2023.5.369
A. Mathew
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.
模$p$Riemann-Hilbert对应关系(协变和逆变形式)与$mathbb相关{F}_p$mathbb谱上的$-’tale滑轮{F}_p$-代数$R$和$R$上的Frobenius模。我们用Breen在完美站点上的消失结果来说明这些对应关系。
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引用次数: 0
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Tunisian Journal of Mathematics
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