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Quasi-linear functionals on locally compact spaces 局部紧空间上的拟线性泛函
Confluentes Mathematici Pub Date : 2019-02-09 DOI: 10.5802/cml.69
S. Butler
{"title":"Quasi-linear functionals on locally compact spaces","authors":"S. Butler","doi":"10.5802/cml.69","DOIUrl":"https://doi.org/10.5802/cml.69","url":null,"abstract":"This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested in quasi-linear functionals on locally compact non-compact spaces or on compact spaces. We study signed and positive quasi-linear functionals paying close attention to singly generated subalgebras. The paper gives representation theorems for quasi-linear functionals on $C_c(X)$ and for bounded quasi-linear functionals on $C_0(X)$ on a locally compact space, and for quasi-linear functionals on $C(X)$ on a compact space. There is an order-preserving bijection between quasi-linear functionals and compact-finite topological measures, which is also \"isometric\" when topological measures are finite. Finally, we further study properties of quasi-linear functionals and give an explicit example of a quasi-linear functional.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85340600","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
Non linear Schrödinger limit of bosonic ground states, again 非线性Schrödinger玻色子基态的极限
Confluentes Mathematici Pub Date : 2019-01-28 DOI: 10.5802/cml.62
N. Rougerie
{"title":"Non linear Schrödinger limit of bosonic ground states, again","authors":"N. Rougerie","doi":"10.5802/cml.62","DOIUrl":"https://doi.org/10.5802/cml.62","url":null,"abstract":"I review an information-theoretic variant of the quantum de Finetti theorem due to Brand{a}o and Harrow and discuss its applications to the topic of bosonic mean-field limits. This leads to slightly improved methods for the derivation of the local non-linear Schr{o}dinger energy functional from many-body quantum mechanics.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72521675","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
Der Satz von Hahn-Banach per Disjunktionselimination 绳结
Confluentes Mathematici Pub Date : 2019-01-01 DOI: 10.5802/cml.57
K. Schlagbauer, P. Schuster, Daniel Wessel
{"title":"Der Satz von Hahn-Banach per Disjunktionselimination","authors":"K. Schlagbauer, P. Schuster, Daniel Wessel","doi":"10.5802/cml.57","DOIUrl":"https://doi.org/10.5802/cml.57","url":null,"abstract":"© Institut Camille Jordan, 2019, tous droits réservés. L’accès aux articles de la revue « Confluentes Mathematici » (http: //cml.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://cml.cedram.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83864425","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
Reversible part of quantum dynamical systems: A review 量子动力系统的可逆部分:综述
Confluentes Mathematici Pub Date : 2019-01-01 DOI: 10.5802/cml.50
Carlo Pandiscia
{"title":"Reversible part of quantum dynamical systems: A review","authors":"Carlo Pandiscia","doi":"10.5802/cml.50","DOIUrl":"https://doi.org/10.5802/cml.50","url":null,"abstract":"In this work a quantum dynamical system (M, Φ, φ) is constituted by a von Neumann algebra M, a unital Schwartz map Φ : M → M and a Φ-invariant normal faithful state φ on M. We will prove that the ergodic properties of a quantum dynamical system are determined by its reversible part (D∞, Φ∞, φ∞); i.e. by a von Neumann sub-algebra D∞ of M, with an automorphism Φ∞ and a normal state φ∞, as the restrictions on D∞. Moreover, if D∞ is a trivial algebra, then the quantum dynamical system is ergodic. Furthermore, we will show some properties of reversible part of the quantum dynamical system, finally we will study its relations with the canonical decomposition of Nagy-Fojas of linear contraction related to a quantum dynamical system.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80563910","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 posteriori error estimates for a fully discrete approximation of Sobolev equations 索博列夫方程的完全离散近似的后验误差估计
Confluentes Mathematici Pub Date : 2019-01-01 DOI: 10.5802/cml.53
S. Nicaise, F. Bekkouche
{"title":"A posteriori error estimates for a fully discrete approximation of Sobolev equations","authors":"S. Nicaise, F. Bekkouche","doi":"10.5802/cml.53","DOIUrl":"https://doi.org/10.5802/cml.53","url":null,"abstract":"L’accès aux articles de la revue « Confluentes Mathematici » (http://cml.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://cml.cedram.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87106095","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
Action de groupe et semi-stabilité du produit tensoriel 张量积的群作用和半稳定性
Confluentes Mathematici Pub Date : 2019-01-01 DOI: 10.5802/cml.55
Gaël Rémond
{"title":"Action de groupe et semi-stabilité du produit tensoriel","authors":"Gaël Rémond","doi":"10.5802/cml.55","DOIUrl":"https://doi.org/10.5802/cml.55","url":null,"abstract":"© Institut Camille Jordan, 2019, tous droits réservés. L’accès aux articles de la revue « Confluentes Mathematici » (http: //cml.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://cml.cedram.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77020325","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
On the distance between homotopy classes in W 1/p,p (𝕊 1 ;𝕊 1 ) 关于W 1/p,p (<s:2> 1; <s:2> 1)中同伦类间的距离
Confluentes Mathematici Pub Date : 2018-09-09 DOI: 10.5802/cml.48
I. Shafrir
{"title":"On the distance between homotopy classes in W 1/p,p (𝕊 1 ;𝕊 1 )","authors":"I. Shafrir","doi":"10.5802/cml.48","DOIUrl":"https://doi.org/10.5802/cml.48","url":null,"abstract":"","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80638285","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
Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de GL n sur un corps local. Représentations cuspidales de niveau zéro. 在局部体上，GL n的Bruhat-Tits建筑上方空间的紧凑支撑上同源。零水平的尖峰表示。
Confluentes Mathematici Pub Date : 2018-09-09 DOI: 10.5802/cml.47
Anis Rajhi
{"title":"Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de GL n sur un corps local. Représentations cuspidales de niveau zéro.","authors":"Anis Rajhi","doi":"10.5802/cml.47","DOIUrl":"https://doi.org/10.5802/cml.47","url":null,"abstract":"","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72679846","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
On probabilistic generalizations of the Nyman-Beurling criterion for the zeta function 关于zeta函数的Nyman-Beurling准则的概率推广
Confluentes Mathematici Pub Date : 2018-05-17 DOI: 10.5802/cml.71
Sébastien Darses, Erwan Hillion
{"title":"On probabilistic generalizations of the Nyman-Beurling criterion for the zeta function","authors":"Sébastien Darses, Erwan Hillion","doi":"10.5802/cml.71","DOIUrl":"https://doi.org/10.5802/cml.71","url":null,"abstract":"The Nyman-Beurling criterion is an approximation problem in the space of square integrable functions on $(0,infty)$, which is equivalent to the Riemann hypothesis. This involves dilations of the fractional part function by factors $theta_kin(0,1)$, $kge1$. We develop probabilistic extensions of the Nyman-Beurling criterion by considering these $theta_k$ as random: this yields new structures and criteria, one of them having a significant overlap with the general strong B'aez-Duarte criterion. %We start here the study of these criteria, with a special focus on exponential and gamma distributions. The main goal of the present paper is the study of the interplay between these probabilistic Nyman-Beurling criteria and the Riemann hypothesis. By means of our probabilistic point of view, we answer a question raised by B'aez-Duarte in 2005. These new structures open the door to calculable determinants.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81818789","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: 5
On Framed Quivers, BPS Invariants and Defects 论框架颤振、BPS不变量和缺陷
Confluentes Mathematici Pub Date : 2018-01-11 DOI: 10.5802/cml.42
M. Cirafici
{"title":"On Framed Quivers, BPS Invariants and Defects","authors":"M. Cirafici","doi":"10.5802/cml.42","DOIUrl":"https://doi.org/10.5802/cml.42","url":null,"abstract":"In this note we review some of the uses of framed quivers to study BPS invariants of Donaldson-Thomas type. We will mostly focus on non-compact Calabi-Yau threefolds. In certain cases the study of these invariants can be approached as a generalized instanton problem in a six dimensional cohomological Yang-Mills theory. One can construct a quantum mechanics model based on a certain framed quiver which locally describes the theory around a generalized instanton solution. The problem is then reduced to the study of the moduli spaces of representations of these quivers. Examples include the affine space and noncommutative crepant resolutions of orbifold singularities. In the second part of the survey we introduce the concepts of defects in physics and argue with a few examples that they give rise to a modified Donaldson-Thomas problem. We mostly focus on divisor defects in six dimensional Yang-Mills theory and their relation with the moduli spaces of parabolic sheaves. In certain cases also this problem can be reformulated in terms of framed quivers.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"32 1","pages":"71-99"},"PeriodicalIF":0.0,"publicationDate":"2018-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75778146","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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