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Boundedness of certain linear operators on twisted Fock spaces 扭曲 Fock 空间上某些线性算子的有界性
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-21 DOI: 10.1007/s00209-024-03500-0
Rahul Garg, Sundaram Thangavelu
{"title":"Boundedness of certain linear operators on twisted Fock spaces","authors":"Rahul Garg, Sundaram Thangavelu","doi":"10.1007/s00209-024-03500-0","DOIUrl":"https://doi.org/10.1007/s00209-024-03500-0","url":null,"abstract":"<p>On the twisted Fock spaces <span>( {mathcal {F}}^lambda ({{mathbb {C}}}^{2n}) )</span> we consider two types of convolution operators <span>( S_varphi ^lambda )</span> and <span>( {widetilde{S}}_varphi ^lambda )</span> associated to an element <span>( varphi in {mathcal {F}}^lambda ({{mathbb {C}}}^{2n}).)</span> We find a necessary and sufficient condition on <span>( varphi )</span> so that <span>( S_varphi ^lambda )</span> (resp. <span>( {widetilde{S}}_varphi ^lambda )</span> ) is bounded on <span>( {mathcal {F}}^lambda ({{mathbb {C}}}^{2n}).)</span> We show that for any given non constant <span>( varphi )</span> at least one of these two operators is unbounded.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"2015 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152539","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}
引用次数: 0
Escaping Fatou components with disjoint hyperbolic limit sets 用互不相交的双曲极限集逃离法图成分
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-20 DOI: 10.1007/s00209-024-03501-z
Veronica Beltrami, Anna Miriam Benini, Alberto Saracco
{"title":"Escaping Fatou components with disjoint hyperbolic limit sets","authors":"Veronica Beltrami, Anna Miriam Benini, Alberto Saracco","doi":"10.1007/s00209-024-03501-z","DOIUrl":"https://doi.org/10.1007/s00209-024-03501-z","url":null,"abstract":"<p>We construct automorphisms of <span>({{mathbb {C}}}^2)</span> of constant Jacobian with a cycle of escaping Fatou components, on which there are exactly two limit functions, both of rank 1. On each such Fatou component, the limit sets for these limit functions are two disjoint hyperbolic subsets of the line at infinity. In the literature there are currently very few examples of automorphisms of <span>({{mathbb {C}}}^2)</span> with rank one limit sets on the boundary of Fatou components. To our knowledge, this is the first example in which such limit sets are hyperbolic, and moreover different limit sets of rank 1 coexist.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152592","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}
引用次数: 0
On sofic approximations of non amenable groups 关于非友好群组的索非近似值
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-20 DOI: 10.1007/s00209-024-03509-5
Ben Hayes, Srivatsav Kunnawalkam Elayavalli
{"title":"On sofic approximations of non amenable groups","authors":"Ben Hayes, Srivatsav Kunnawalkam Elayavalli","doi":"10.1007/s00209-024-03509-5","DOIUrl":"https://doi.org/10.1007/s00209-024-03509-5","url":null,"abstract":"<p>In this paper we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any automorphism of the universal sofic group. This addresses a question of Pǎunescu and generalizes the Elek–Szabo uniqueness theorem for sofic approximations.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"75 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152593","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}
引用次数: 0
On the union of homogeneous symmetric Cantor set with its translations 论同质对称康托集合与其平移的结合
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-16 DOI: 10.1007/s00209-024-03499-4
Derong Kong, Wenxia Li, Zhiqiang Wang, Yuanyuan Yao, Yunxiu Zhang
{"title":"On the union of homogeneous symmetric Cantor set with its translations","authors":"Derong Kong, Wenxia Li, Zhiqiang Wang, Yuanyuan Yao, Yunxiu Zhang","doi":"10.1007/s00209-024-03499-4","DOIUrl":"https://doi.org/10.1007/s00209-024-03499-4","url":null,"abstract":"<p>Fix a positive integer <i>N</i> and a real number <span>(0&lt; beta &lt; 1/(N+1))</span>. Let <span>(Gamma )</span> be the homogeneous symmetric Cantor set generated by the IFS </p><span>$$begin{aligned} Bigg { phi _i(x)=beta x + i frac{1-beta }{N}: i=0,1,ldots , N Bigg }. end{aligned}$$</span><p>For <span>(min mathbb {Z}_+)</span> we show that there exist infinitely many translation vectors <span>({textbf{t}}=(t_0,t_1,ldots , t_m))</span> with <span>(0=t_0&lt;t_1&lt;cdots &lt;t_m)</span> such that the union <span>(bigcup _{j=0}^m(Gamma +t_j))</span> is a self-similar set. Furthermore, for <span>(0&lt; beta &lt; 1/(2N+1))</span>, we give a finite algorithm to determine whether the union <span>(bigcup _{j=0}^m(Gamma +t_j))</span> is a self-similar set for any given vector <span>({textbf{t}})</span>. Our characterization relies on determining whether some related directed graph has no cycles, or whether some related adjacency matrix is nilpotent.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"54 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058730","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}
引用次数: 0
A weighted one-level density of the non-trivial zeros of the Riemann zeta-function 黎曼zeta函数非琐零点的加权一级密度
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-13 DOI: 10.1007/s00209-024-03496-7
Sandro Bettin, Alessandro Fazzari
{"title":"A weighted one-level density of the non-trivial zeros of the Riemann zeta-function","authors":"Sandro Bettin, Alessandro Fazzari","doi":"10.1007/s00209-024-03496-7","DOIUrl":"https://doi.org/10.1007/s00209-024-03496-7","url":null,"abstract":"<p>We compute the one-level density of the non-trivial zeros of the Riemann zeta-function weighted by <span>(|zeta (frac{1}{2}+it)|^{2k})</span> for <span>(k=1)</span> and, for test functions with Fourier support in <span>((-frac{1}{2},frac{1}{2}))</span>, for <span>(k=2)</span>. As a consequence, for <span>(k=1,2)</span>, we deduce under the Riemann hypothesis that <span>(T(log T)^{1-k^2+o(1)})</span> non-trivial zeros of <span>(zeta )</span>, of imaginary parts up to <i>T</i>, are such that <span>(zeta )</span> attains a value of size <span>((log T)^{k+o(1)})</span> at a point which is within <span>(O(1/log T))</span> from the zero.\u0000</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"43 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931964","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}
引用次数: 0
Regularity for the Monge–Ampère equation by doubling 蒙日-安培方程的正则性倍增
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-13 DOI: 10.1007/s00209-024-03508-6
Ravi Shankar, Yu Yuan
{"title":"Regularity for the Monge–Ampère equation by doubling","authors":"Ravi Shankar, Yu Yuan","doi":"10.1007/s00209-024-03508-6","DOIUrl":"https://doi.org/10.1007/s00209-024-03508-6","url":null,"abstract":"<p>We give a new proof for the interior regularity of strictly convex solutions of the Monge–Ampère equation. Our approach uses a doubling inequality for the Hessian in terms of the extrinsic distance function on the maximal Lagrangian submanifold determined by the potential equation.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"77 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932023","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}
引用次数: 0
Extrinsic geometry of calibrated submanifolds 校准子曼形体的外几何学
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-13 DOI: 10.1007/s00209-024-03503-x
Spiro Karigiannis, Lucía Martín-Merchán
{"title":"Extrinsic geometry of calibrated submanifolds","authors":"Spiro Karigiannis, Lucía Martín-Merchán","doi":"10.1007/s00209-024-03503-x","DOIUrl":"https://doi.org/10.1007/s00209-024-03503-x","url":null,"abstract":"<p>Given a calibration <span>(alpha )</span> whose stabilizer acts transitively on the Grassmanian of calibrated planes, we introduce a nontrivial Lie-theoretic condition on <span>(alpha )</span>, which we call <i>compliancy</i>, and show that this condition holds for many interesting geometric calibrations, including Kähler, special Lagrangian, associative, coassociative, and Cayley. We determine a sufficient condition that ensures compliancy of <span>(alpha )</span>, we completely characterize compliancy in terms of properties of a natural involution determined by a calibrated plane, and we relate compliancy to the geometry of the calibrated Grassmanian. The condition that a Riemannian immersion <span>(iota :L rightarrow M)</span> be calibrated is a first order condition. By contrast, its extrinsic geometry, given by the second fundamental form <i>A</i> and the induced tangent and normal connections <span>(nabla )</span> on <i>TL</i> and <i>D</i> on <i>NL</i>, respectively, is second order information. We characterize the conditions imposed on the extrinsic geometric data <span>((A, nabla , D))</span> when the Riemannian immersion <span>(iota :L rightarrow M)</span> is calibrated with respect to a calibration <span>(alpha )</span> on <i>M</i> which is both <i>parallel</i> and <i>compliant</i>. This motivate the definition of an <i>infinitesimally calibrated</i> Riemannian immersion, generalizing the classical notion of a superminimal surface in <span>({mathbb {R}}^4)</span>.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"62 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932022","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}
引用次数: 0
Fino–Vezzoni conjecture on Lie algebras with abelian ideals of codimension two 关于具有二维无边际簇的列阵的菲诺-维佐尼猜想
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-12 DOI: 10.1007/s00209-024-03506-8
Kexiang Cao, Fangyang Zheng
{"title":"Fino–Vezzoni conjecture on Lie algebras with abelian ideals of codimension two","authors":"Kexiang Cao, Fangyang Zheng","doi":"10.1007/s00209-024-03506-8","DOIUrl":"https://doi.org/10.1007/s00209-024-03506-8","url":null,"abstract":"<p>In this paper, we confirm the Fino–Vezzoni Conjecture for unimodular Lie algebras which contain abelian ideals of codimension two, a natural generalization to the class of almost abelian Lie algebras. This provides new evidence towards the validity of the conjecture on a very special type of 3-step solvmanifolds.\u0000</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"105 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932028","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}
引用次数: 0
Gap for geometric canonical height functions 几何标准高度函数的差距
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-11 DOI: 10.1007/s00209-024-03502-y
Yugang Zhang
{"title":"Gap for geometric canonical height functions","authors":"Yugang Zhang","doi":"10.1007/s00209-024-03502-y","DOIUrl":"https://doi.org/10.1007/s00209-024-03502-y","url":null,"abstract":"<p>We prove the existence of a gap around zero for canonical height functions associated with endomorphisms of projective spaces defined over complex function fields. We also prove that if the rational points of height zero are Zariski dense, then the endomorphism is birationally isotrivial. As a corollary, by a result of S. Cantat and J. Xie, we have a geometric Northcott property on projective plane in the same spirit of results of R. Benedetto, M. Baker and L. Demarco on the projective line.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"130 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931957","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}
引用次数: 0
The Monge–Ampère equation for $$(n-1)$$ -quaternionic PSH functions on a hyperKähler manifold 超凯勒流形上$$(n-1)$$四元 PSH 函数的蒙日-安培方程
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-10 DOI: 10.1007/s00209-024-03504-w
Jixiang Fu, Xin Xu, Dekai Zhang
{"title":"The Monge–Ampère equation for $$(n-1)$$ -quaternionic PSH functions on a hyperKähler manifold","authors":"Jixiang Fu, Xin Xu, Dekai Zhang","doi":"10.1007/s00209-024-03504-w","DOIUrl":"https://doi.org/10.1007/s00209-024-03504-w","url":null,"abstract":"<p>We prove the existence of a unique smooth solution to the quaternionic Monge–Ampère equation for <span>((n-1))</span>-quaternionic plurisubharmonic (psh) functions on a compact hyperKähler manifold and thus obtain solutions to the quaternionic form-type equation. We derive the <span>(C^0)</span> estimate by establishing a Cherrier-type inequality as in Tosatti and Weinkove (J Am Math Soc 30(2):311–346, 2017). By adopting the approach of Dinew and Sroka (Geom Funct Anal 33(4):875–911, 2023) to our context, we obtain the <span>(C^1)</span> and <span>(C^2)</span> estimates without assuming the flatness of underlying hyperKähler metric comparing to the previous result Gentili and Zhang (J Geom Anal 32:9, 2022).</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"36 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932036","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}
引用次数: 0
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