Pub Date : 2019-08-19DOI: 10.2140/tunis.2020.2.851
Franccois Vigneron
We give an elementary proof of the classical Hardy inequality on any Carnot group, using only integration by parts and a fine analysis of the commutator structure, which was not deemed possible until now. We also discuss the conditions under which this technique can be generalized to deal with hypoelliptic families of vector fields, which, in this case, leads to an open problem regarding the symbol properties of the gauge norm.
{"title":"A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields","authors":"Franccois Vigneron","doi":"10.2140/tunis.2020.2.851","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.851","url":null,"abstract":"We give an elementary proof of the classical Hardy inequality on any Carnot group, using only integration by parts and a fine analysis of the commutator structure, which was not deemed possible until now. We also discuss the conditions under which this technique can be generalized to deal with hypoelliptic families of vector fields, which, in this case, leads to an open problem regarding the symbol properties of the gauge norm.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.851","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41894538","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}
We build model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences determined by families of subgroups. In particular, by specifying to the family of graph subgroups (or, more generally, one of the indexing systems of Blumberg-Hill), we obtain model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences are determined by norm map data.
{"title":"Homotopy theory of equivariant operads with fixed colors","authors":"P. Bonventre, L. Pereira","doi":"10.2140/tunis.2022.4.87","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.87","url":null,"abstract":"We build model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences determined by families of subgroups. In particular, by specifying to the family of graph subgroups (or, more generally, one of the indexing systems of Blumberg-Hill), we obtain model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences are determined by norm map data.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43481495","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 : 2019-05-20DOI: 10.2140/tunis.2021.3.843
K. Hermann, M. Voit
Consider Jacobi random matrix ensembles with the distributions $$c_{k_1,k_2,k_3}prod_{1leq i -1leq x_1le ...le x_Nleq 1}.$$ For $(k_1,k_2,k_3)=kappacdot (a,b,1)$ with $a,b>0$ fixed, we derive a central limit theorem for the distributions above for $kappatoinfty$. The drift and the inverse of the limit covariance matrix are expressed in terms of the zeros of classical Jacobi polynomials. We also rewrite the CLT in trigonometric form and determine the eigenvalues and eigenvectors of the limit covariance matrices. These results are related to corresponding limits for $beta$-Hermite and $beta$-Laguerre ensembles for $betatoinfty$ by Dumitriu and Edelman and by Voit.
考虑具有$$c_{k_1,k_2,k_3}prod_{1leq i -1leq x_1le ...le x_Nleq 1}.$$分布的Jacobi随机矩阵集合对于$a,b>0$固定的$(k_1,k_2,k_3)=kappacdot (a,b,1)$，我们为$kappatoinfty$导出了上述分布的中心极限定理。极限协方差矩阵的漂移和逆用经典雅可比多项式的零点表示。我们还将CLT写成三角函数形式，并确定了极限协方差矩阵的特征值和特征向量。这些结果与Dumitriu和Edelman以及Voit对$betatoinfty$的$beta$ -Hermite和$beta$ -Laguerre系综的相应极限有关。
{"title":"Limit theorems for Jacobi ensembles with large parameters","authors":"K. Hermann, M. Voit","doi":"10.2140/tunis.2021.3.843","DOIUrl":"https://doi.org/10.2140/tunis.2021.3.843","url":null,"abstract":"Consider Jacobi random matrix ensembles with the distributions $$c_{k_1,k_2,k_3}prod_{1leq i -1leq x_1le ...le x_Nleq 1}.$$ For $(k_1,k_2,k_3)=kappacdot (a,b,1)$ with $a,b>0$ fixed, we derive a central limit theorem for the distributions above for $kappatoinfty$. The drift and the inverse of the limit covariance matrix are expressed in terms of the zeros of classical Jacobi polynomials. We also rewrite the CLT in trigonometric form and determine the eigenvalues and eigenvectors of the limit covariance matrices. These results are related to corresponding limits for $beta$-Hermite and $beta$-Laguerre ensembles for $betatoinfty$ by Dumitriu and Edelman and by Voit.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46610018","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 : 2019-05-08DOI: 10.2140/tunis.2022.4.203
Y. Wakabayashi
The aim of the present paper is to provide a new aspect of the $p$-adic Teichmuller theory established by S. Mochizuki. We study the symplectic geometry of the $p$-adic formal stacks $widehat{mathcal{M}}_{g, mathbb{Z}_p}$ (= the moduli classifying $p$-adic formal curves of fixed genus $g>1$) and $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ (= the moduli classifying $p$-adic formal curves of genus $g$ equipped with an indigenous bundle). A major achievement in the (classical) $p$-adic Teichmuller theory is the construction of the locus $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}}$ in $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ classifying $p$-adic canonical liftings of ordinary nilpotent indigenous bundles. The formal stack $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}}$ embodies a $p$-adic analogue of uniformization of hyperbolic Riemann surfaces, as well as a hyperbolic analogue of Serre-Tate theory of ordinary abelian varieties. In the present paper, the canonical symplectic structure on the cotangent bundle $T^vee_{mathbb{Z}_p} widehat{mathcal{M}}_{g, mathbb{Z}_p}$ of $widehat{mathcal{M}}_{g, mathbb{Z}_p}$ is compared to Goldman's symplectic structure defined on $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ after base-change by the projection $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}} rightarrow widehat{mathcal{M}}_{g, mathbb{Z}_p}$. We can think of this comparison as a $p$-adic analogue of certain results in the theory of projective structures on Riemann surfaces proved by S. Kawai and other mathematicians.
{"title":"Symplectic geometry of p-adic Teichmüller\u0000uniformization for ordinary nilpotent indigenous bundles","authors":"Y. Wakabayashi","doi":"10.2140/tunis.2022.4.203","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.203","url":null,"abstract":"The aim of the present paper is to provide a new aspect of the $p$-adic Teichmuller theory established by S. Mochizuki. We study the symplectic geometry of the $p$-adic formal stacks $widehat{mathcal{M}}_{g, mathbb{Z}_p}$ (= the moduli classifying $p$-adic formal curves of fixed genus $g>1$) and $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ (= the moduli classifying $p$-adic formal curves of genus $g$ equipped with an indigenous bundle). A major achievement in the (classical) $p$-adic Teichmuller theory is the construction of the locus $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}}$ in $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ classifying $p$-adic canonical liftings of ordinary nilpotent indigenous bundles. The formal stack $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}}$ embodies a $p$-adic analogue of uniformization of hyperbolic Riemann surfaces, as well as a hyperbolic analogue of Serre-Tate theory of ordinary abelian varieties. In the present paper, the canonical symplectic structure on the cotangent bundle $T^vee_{mathbb{Z}_p} widehat{mathcal{M}}_{g, mathbb{Z}_p}$ of $widehat{mathcal{M}}_{g, mathbb{Z}_p}$ is compared to Goldman's symplectic structure defined on $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ after base-change by the projection $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}} rightarrow widehat{mathcal{M}}_{g, mathbb{Z}_p}$. We can think of this comparison as a $p$-adic analogue of certain results in the theory of projective structures on Riemann surfaces proved by S. Kawai and other mathematicians.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44026996","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}
{"title":"On the irreducibility of some induced representations of real reductive Lie groups","authors":"W. Gan, Atsushi Ichino","doi":"10.2140/TUNIS.2019.1.73","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.73","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.73","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49219077","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}
{"title":"Welcome to the Tunisian Journal of Mathematics","authors":"A. Abbes, A. Baklouti","doi":"10.2140/TUNIS.2019.1.1","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.1","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571112","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 : 2019-01-01DOI: 10.2140/TUNIS.2019.1.321
M. Derridj
{"title":"Local estimates for Hörmander’s operators\u0000with Gevrey coefficients and application to the regularity of their Gevrey\u0000vectors","authors":"M. Derridj","doi":"10.2140/TUNIS.2019.1.321","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.321","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571572","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 : 2019-01-01DOI: 10.2140/TUNIS.2019.1.561
Y. Brenier
We establish the geometric origin ot the nonlinear heat equation with arct-angential nonlinearity: ∂ t D = ∆(arctan D) by deriving it, together and in du-ality with the mean curvature flow equation, from the minimal surface equation in Minkowski space-time, through a suitable quadratic change of time. After examining various properties of the arctangential heat equation (in particular through its optimal transport interpretation a la Otto and its relationship with the Born-Infeld theory of Electromagnetism), we shortly discuss its possible use for image processing, once written in non-conservative form and properly discretized.
通过适当的二次时间变化，从闵可夫斯基时空的最小曲面方程出发，推导出与平均曲率流动方程对偶的，具有arcarcential非线性的非线性热方程∂t D =∆(arctan D)的几何原点。在考察了切向热方程的各种性质(特别是通过其最优输运解释和它与波恩-因菲尔德电磁学理论的关系)之后，我们将简要讨论它在图像处理中的可能用途，一旦以非保守形式书写并适当离散。
{"title":"Geometric origin and some properties of the arctangential heat equation","authors":"Y. Brenier","doi":"10.2140/TUNIS.2019.1.561","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.561","url":null,"abstract":"We establish the geometric origin ot the nonlinear heat equation with arct-angential nonlinearity: ∂ t D = ∆(arctan D) by deriving it, together and in du-ality with the mean curvature flow equation, from the minimal surface equation in Minkowski space-time, through a suitable quadratic change of time. After examining various properties of the arctangential heat equation (in particular through its optimal transport interpretation a la Otto and its relationship with the Born-Infeld theory of Electromagnetism), we shortly discuss its possible use for image processing, once written in non-conservative form and properly discretized.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.561","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571716","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 : 2019-01-01DOI: 10.2140/TUNIS.2019.1.455
A. Langer, T. Zink
This is the final version. Available from Tunisian Mathematical Society / MSP via the DOI in this record.
这是最终版本。可通过内政部从突尼斯数学学会/MSP获得。
{"title":"Grothendieck–Messing deformation theory for\u0000varieties of K3 type","authors":"A. Langer, T. Zink","doi":"10.2140/TUNIS.2019.1.455","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.455","url":null,"abstract":"This is the final version. Available from Tunisian Mathematical Society / MSP via the DOI in this record.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.455","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45960335","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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