{"title":"Spectral deviation of concentration operators for the short-time Fourier transform","authors":"F. Marceca, J. Romero","doi":"10.4064/sm220214-17-10","DOIUrl":"https://doi.org/10.4064/sm220214-17-10","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"196 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70524748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Let X be a real Banach space. For a non-empty finite subset F and closed convex subset V of X , we denote by rad X ( F ) , rad V ( F ) , cent X ( F ) and d ( V, cent X ( F )) the Chebyshev radius of F in X , the restricted Chebyshev radius of F in V , the set of Chebyshev centers of F in X and the distance between the sets V and cent X ( F ) respectively. We prove that X is an L 1 -predual space if and only if for each four-point subset F of X and non-empty closed convex subset V of X , rad V ( F ) = rad X ( F ) + d ( V, cent X ( F )) . Moreover, we explicitly describe the Chebyshev centers of a compact subset of an L 1 - predual space. Various new characterizations of ideals in an L 1 -predual space are also obtained. In particular, for a compact Hausdorff space S and a subspace A of C ( S ) which contains the constant function 1 and separates the points of S , we prove that the state space of A is a Choquet simplex if and only if d ( A , cent C ( S ) ( F )) = 0 for every four-point subset F of A . We also derive characterizations for a compact convex subset of a locally convex topological vector space to be a Choquet simplex.
． 设X是一个实巴拿赫空间。对于一个非空有限子集F (X)和闭凸子集,我们通过rad X (F)表示,rad V (F),分X (F)和d (V,分X (F))的切比雪夫半径F在X, V F的切比雪夫半径限制,F组切比雪夫中心的X和之间的距离分别设置V和分X (F)。证明X是一个l1 -预偶空间当且仅当对于X的每个四点子集F和X的非空闭凸子集V, rad V (F) = rad X (F) + d (V, cent X (F))。此外，我们明确地描述了一个l1 -前偶空间的紧子集的切比雪夫中心。得到了理想在l1 -前偶空间中的各种新的表征。特别地，对于紧化Hausdorff空间S和C (S)的子空间a(包含常数函数1并分隔S的点)，我们证明了当且仅当d (a, C (S) (F)) = 0时，a的状态空间是Choquet单纯形。我们还推导了局部凸拓扑向量空间的紧凸子集为Choquet单纯形的刻画。
{"title":"Some geometrical characterizations of $L_1$-predual spaces","authors":"Teena Thomas","doi":"10.4064/sm220608-4-11","DOIUrl":"https://doi.org/10.4064/sm220608-4-11","url":null,"abstract":". Let X be a real Banach space. For a non-empty finite subset F and closed convex subset V of X , we denote by rad X ( F ) , rad V ( F ) , cent X ( F ) and d ( V, cent X ( F )) the Chebyshev radius of F in X , the restricted Chebyshev radius of F in V , the set of Chebyshev centers of F in X and the distance between the sets V and cent X ( F ) respectively. We prove that X is an L 1 -predual space if and only if for each four-point subset F of X and non-empty closed convex subset V of X , rad V ( F ) = rad X ( F ) + d ( V, cent X ( F )) . Moreover, we explicitly describe the Chebyshev centers of a compact subset of an L 1 - predual space. Various new characterizations of ideals in an L 1 -predual space are also obtained. In particular, for a compact Hausdorff space S and a subspace A of C ( S ) which contains the constant function 1 and separates the points of S , we prove that the state space of A is a Choquet simplex if and only if d ( A , cent C ( S ) ( F )) = 0 for every four-point subset F of A . We also derive characterizations for a compact convex subset of a locally convex topological vector space to be a Choquet simplex.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Closed ideals in weighted big Lipschitz algebras of analytic functions","authors":"B. Bouya, M. Zarrabi","doi":"10.4064/sm210401-25-10","DOIUrl":"https://doi.org/10.4064/sm210401-25-10","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70515748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Embedding of fractional Sobolev spaces is equivalent to regularity of the measure","authors":"P. Górka, Artur Słabuszewski","doi":"10.4064/sm220304-2-7","DOIUrl":"https://doi.org/10.4064/sm220304-2-7","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70524822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Approximation properties in terms of Lipschitz maps","authors":"Mingu Jung, Ju Myung Kim","doi":"10.4064/sm220314-19-8","DOIUrl":"https://doi.org/10.4064/sm220314-19-8","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, the Monge–Kantorovich problem is considered in infinite dimensions on an abstract Wiener space ( W, H, µ ) , where H is the Cameron–Martin space and µ is the Gaussian measure. We study the regularity of optimal transport maps with a quadratic cost function assuming that both initial and target measures have a strictly positive Radon–Nikodym density with respect to µ . Under some conditions on the density functions, the forward and backward transport maps can be written in terms of Sobolev derivatives of so-called Monge–Brenier maps, or Monge potentials. We show the Sobolev regularity of the backward potential under the assumption that the density of the initial measure is log-concave and prove that the backward potential solves the Monge–Ampère equation.
{"title":"Regularity of the backward Monge potential and the Monge–Ampère equation on Wiener space","authors":"M. Çağlar, I. Demirel","doi":"10.4064/sm210906-2-5","DOIUrl":"https://doi.org/10.4064/sm210906-2-5","url":null,"abstract":". In this paper, the Monge–Kantorovich problem is considered in infinite dimensions on an abstract Wiener space ( W, H, µ ) , where H is the Cameron–Martin space and µ is the Gaussian measure. We study the regularity of optimal transport maps with a quadratic cost function assuming that both initial and target measures have a strictly positive Radon–Nikodym density with respect to µ . Under some conditions on the density functions, the forward and backward transport maps can be written in terms of Sobolev derivatives of so-called Monge–Brenier maps, or Monge potentials. We show the Sobolev regularity of the backward potential under the assumption that the density of the initial measure is log-concave and prove that the backward potential solves the Monge–Ampère equation.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a one-parameter continuous family of pairs of complementary boundary conditions","authors":"A. Bobrowski, Elżbieta Ratajczyk","doi":"10.4064/sm210618-3-11","DOIUrl":"https://doi.org/10.4064/sm210618-3-11","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：