发布求助
文献互助 智能选刊 最新文献

Mathematische Zeitschrift最新文献

筛选
英文 中文
Jordan mating is always possible for polynomials 多项式总是可以进行乔丹交配
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-15 DOI: 10.1007/s00209-024-03465-0
{"title":"Jordan mating is always possible for polynomials","authors":"","doi":"10.1007/s00209-024-03465-0","DOIUrl":"https://doi.org/10.1007/s00209-024-03465-0","url":null,"abstract":"<h3>Abstract</h3> <p>Suppose <em>f</em> and <em>g</em> are two post-critically finite polynomials of degree <span> <span>(d_1)</span> </span> and <span> <span>(d_2)</span> </span> respectively and suppose both of them have a finite super-attracting fixed point of degree <span> <span>(d_0)</span> </span>. We prove that one can always construct a rational map <em>R</em> of degree <span> <span>$$begin{aligned} D = d_1 + d_2 - d_0 end{aligned}$$</span> </span>by gluing <em>f</em> and <em>g</em> along the Jordan curve boundaries of the immediate super-attracting basins. The result can be used to construct many rational maps with interesting dynamics.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154301","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
Bloom weighted bounds for sparse forms associated to commutators 与换元子相关的稀疏形式的布卢姆加权边界
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-15 DOI: 10.1007/s00209-024-03471-2
Andrei K. LernerEmiel LoristSheldy Ombrosi
{"title":"Bloom weighted bounds for sparse forms associated to commutators","authors":"Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi","doi":"10.1007/s00209-024-03471-2","DOIUrl":"https://doi.org/10.1007/s00209-024-03471-2","url":null,"abstract":"<p>In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal and off-diagonal cases. As an application, we obtain new Bloom bounds for commutators of (maximal) rough homogeneous singular integrals and the Bochner–Riesz operator at the critical index. We also raise the question about the sharpness of our estimates. In particular we obtain the surprising fact that even in the case of Calderón–Zygmund operators, the previously known quantitative Bloom bounds are not sharp for the second and higher order commutators.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"147 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154118","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
Ill-posedness for the Half wave Schrödinger equation 半波薛定谔方程的假定性
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-15 DOI: 10.1007/s00209-024-03452-5
Isao Kato
{"title":"Ill-posedness for the Half wave Schrödinger equation","authors":"Isao Kato","doi":"10.1007/s00209-024-03452-5","DOIUrl":"https://doi.org/10.1007/s00209-024-03452-5","url":null,"abstract":"<p>We study the Cauchy problem for the half wave Schrödinger equation introduced by Xu [9]. There are some well-posedness results for the equation, however there is no ill-posedness result. We focus on the scale critical space and obtain the ill-posedness in the super-critical or at the critical space under certain condition. The proofs in the super-critical space are based on the argument established by Christ, Colliander and Tao [4]. More precisely, we analyze dispersionless equation with smooth initial data, namely the Schwartz function and it is locally well-posed in some weighted Sobolev space. We construct the solution for the half wave Schrödinger equation by using the solution for the dispersionless equation and we can exploit the norm inflation or the decoherence properties. For the critical space, we use the standing wave solution, which was proved the existence by Bahri, Ibrahim and Kikuchi [1].</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"30 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154237","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
Cohomology and geometry of Deligne–Lusztig varieties for $$textrm{GL}_n$$ $$textrm{GL}_n$ 的德利涅-卢茨蒂格变体的同调与几何
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-14 DOI: 10.1007/s00209-024-03455-2
Yingying Wang
{"title":"Cohomology and geometry of Deligne–Lusztig varieties for $$textrm{GL}_n$$","authors":"Yingying Wang","doi":"10.1007/s00209-024-03455-2","DOIUrl":"https://doi.org/10.1007/s00209-024-03455-2","url":null,"abstract":"<p>We give a description of the cohomology groups of the structure sheaf on smooth compactifications <span>(overline{X}(w))</span> of Deligne–Lusztig varieties <i>X</i>(<i>w</i>) for <span>(textrm{GL}_n)</span>, for all elements <i>w</i> in the Weyl group. As a consequence, we obtain the <span>(textrm{mod} p^m)</span> and integral <i>p</i>-adic étale cohomology of <span>(overline{X}(w))</span>. Moreover, using our result for <span>(overline{X}(w))</span> and a spectral sequence associated to a stratification of <span>(overline{X}(w))</span>, we deduce the <span>(textrm{mod} p^m)</span> and integral <i>p</i>-adic étale cohomology with compact support of <i>X</i>(<i>w</i>). In our proof of the main theorem, in addition to considering the Demazure–Hansen smooth compactifications of <i>X</i>(<i>w</i>), we show that a similar class of constructions provide smooth compactifications of <i>X</i>(<i>w</i>) in the case of <span>(textrm{GL}_n)</span>. Furthermore, we show in the appendix that the Zariski closure of <i>X</i>(<i>w</i>), for any connected reductive group <i>G</i> and any <i>w</i>, has pseudo-rational singularities.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154114","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
D-finiteness, rationality, and height III: multivariate Pólya–Carlson dichotomy D 因性、合理性和身高 III：多元波利亚-卡尔森二分法
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-14 DOI: 10.1007/s00209-024-03470-3
Shaoshi ChenUmberto ZannierJason P. BellKhoa D. Nguyen
{"title":"D-finiteness, rationality, and height III: multivariate Pólya–Carlson dichotomy","authors":"Jason P. Bell, Shaoshi Chen, Khoa D. Nguyen, Umberto Zannier","doi":"10.1007/s00209-024-03470-3","DOIUrl":"https://doi.org/10.1007/s00209-024-03470-3","url":null,"abstract":"<p>We prove a result that can be seen as an analogue of the Pólya–Carlson theorem for multivariate D-finite power series with coefficients in <span>(bar{mathbb {Q}})</span>. In the special case that the coefficients are algebraic integers, our main result says that if </p><span>$$begin{aligned} F(x_1,ldots ,x_m)=sum f(n_1,ldots ,n_m)x_1^{n_1}cdots x_m^{n_m} end{aligned}$$</span><p>is a D-finite power series in <i>m</i> variables with algebraic integer coefficients and if the logarithmic Weil height of <span>(f(n_1,ldots ,n_m))</span> is <span>(o(n_1+cdots +n_m))</span>, then <i>F</i> is a rational function and, up to scalar multiplication, every irreducible factor of the denominator of <i>F</i> has the form <span>(1-zeta x_1^{q_1}cdots x_m^{q_m})</span> where <span>(zeta )</span> is a root of unity and <span>(q_1,ldots ,q_m)</span> are nonnegative integers, not all of which are zero.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"68 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154300","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
Matrix Kloosterman sums modulo prime powers 矩阵克罗斯特曼求和的质幂模数
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-14 DOI: 10.1007/s00209-024-03467-y
M. Erdélyi
{"title":"Matrix Kloosterman sums modulo prime powers","authors":"M. Erdélyi, Á. Tóth, G. Zábrádi","doi":"10.1007/s00209-024-03467-y","DOIUrl":"https://doi.org/10.1007/s00209-024-03467-y","url":null,"abstract":"<p>We give optimal bounds for matrix Kloosterman sums modulo prime powers extending earlier work of the first two authors on the case of prime moduli. These exponential sums arise in the theory of the horocyclic flow on <span>(GL_n)</span>.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"123 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154243","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
Whittaker categories and the minimal nilpotent finite W-algebras for $$mathfrak {sl}_{n+1}$$ 惠特克范畴和 $$mathfrak {sl}_{n+1}$ 的最小无钾性有限 W 矩阵
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-12 DOI: 10.1007/s00209-024-03469-w
Genqiang LiuYang Li
{"title":"Whittaker categories and the minimal nilpotent finite W-algebras for $$mathfrak {sl}_{n+1}$$","authors":"Genqiang Liu, Yang Li","doi":"10.1007/s00209-024-03469-w","DOIUrl":"https://doi.org/10.1007/s00209-024-03469-w","url":null,"abstract":"<p>For any <span>({textbf{a}}=(a_1,dots ,a_n)in {mathbb {C}}^n)</span>, we introduce a Whittaker category <span>({mathcal {H}}_{{textbf{a}}})</span> whose objects are <span>(mathfrak {sl}_{n+1})</span>-modules <i>M</i> such that <span>(e_{0i}-a_i)</span> acts locally nilpotently on <i>M</i> for all <span>(i in {1,dots ,n})</span>, and the subspace <span>(textrm{wh}_{{textbf{a}}}(M)={vin M mid e_{0i} v=a_iv, i=1,dots ,n})</span> is finite dimensional. In this paper, we first give a tensor product decomposition <span>(U_S=Wotimes B)</span> of the localization <span>(U_S)</span> of <span>(U(mathfrak {sl}_{n+1}))</span> with respect to the Ore subset <i>S</i> generated by <span>(e_{01},dots , e_{0n})</span>. We show that the associative algebra <i>W</i> is isomorphic to the type <span>(A_n)</span> finite <i>W</i>-algebra <i>W</i>(<i>e</i>) defined by a minimal nilpotent element <i>e</i> in <span>(mathfrak {sl}_{n+1})</span>. Then using <i>W</i>-modules as a bridge, we show that each block with a generalized central character of <span>({mathcal {H}}_{{textbf{1}}})</span> is equivalent to the corresponding block of the cuspidal category <span>({mathcal {C}})</span>, which is completely characterized by Grantcharov and Serganova. As a consequence, each regular integral block of <span>({mathcal {H}}_{{textbf{1}}})</span> and the category of finite dimensional modules over <i>W</i>(<i>e</i>) can be described by a well-studied quiver with certain quadratic relations.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"49 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115669","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
Nonempty interior of configuration sets via microlocal partition optimization 通过微局部分区优化实现配置集的非空内部
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-12 DOI: 10.1007/s00209-024-03466-z
Allan Greenleaf, Alex Iosevich, Krystal Taylor
{"title":"Nonempty interior of configuration sets via microlocal partition optimization","authors":"Allan Greenleaf, Alex Iosevich, Krystal Taylor","doi":"10.1007/s00209-024-03466-z","DOIUrl":"https://doi.org/10.1007/s00209-024-03466-z","url":null,"abstract":"<p>We prove new results of Mattila–Sjölin type, giving lower bounds on Hausdorff dimensions of thin sets <span>(Esubset mathbb {R}^d)</span> ensuring that various <i>k</i>-point configuration sets, generated by elements of <i>E</i>, have nonempty interior. The dimensional thresholds in our previous work (Greenleaf et al., Mathematika 68(1):163–190, 2022) were dictated by associating to a configuration function a family of generalized Radon transforms, and then optimizing <span>(L^2)</span>-Sobolev estimates for them over all nontrivial bipartite partitions of the <i>k</i> points. In the current work, we extend this by allowing the optimization to be done locally over the configuration’s incidence relation, or even microlocally over the conormal bundle of the incidence relation. We use this approach to prove Mattila–Sjölin type results for (i) areas of subtriangles determined by quadrilaterals and pentagons in a set <span>(Esubset mathbb {R}^2)</span>; (ii) pairs of ratios of distances of 4-tuples in <span>(mathbb {R}^d)</span>; and (iii) similarity classes of triangles in <span>(mathbb {R}^d)</span>, as well as to (iv) give a short proof of Palsson and Romero Acosta’s result on congruence classes of triangles in <span>(mathbb {R}^d)</span>.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"83 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115298","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
Canonical integral operators on the Fock space 福克空间上的典型积分算子
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-12 DOI: 10.1007/s00209-024-03463-2
Kehe ZhuXingtang Dong
{"title":"Canonical integral operators on the Fock space","authors":"Xingtang Dong, Kehe Zhu","doi":"10.1007/s00209-024-03463-2","DOIUrl":"https://doi.org/10.1007/s00209-024-03463-2","url":null,"abstract":"<p>In this paper we introduce and study a two-parameter family of integral operators on the Fock space <span>(F^2({mathbb {C}}))</span>. We determine exactly when these operators are bounded and when they are unitary. We show that, under the Bargmann transform, these operators include the classical linear canonical transforms as special cases. As an application, we obtain a new unitary projective representation for the special linear group <span>(SL(2,{mathbb {R}}))</span> on the Fock space.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140117601","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
Rank-one perturbations and norm-attaining operators 一阶扰动和有规范的算子
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-03-08 DOI: 10.1007/s00209-024-03458-z
{"title":"Rank-one perturbations and norm-attaining operators","authors":"","doi":"10.1007/s00209-024-03458-z","DOIUrl":"https://doi.org/10.1007/s00209-024-03458-z","url":null,"abstract":"<h3>Abstract</h3> <p>The main goal of this article is to show that for every (reflexive) infinite-dimensional Banach space <em>X</em> there exists a reflexive Banach space <em>Y</em> and <span> <span>(T, R in mathcal {L}(X,Y))</span> </span> such that <em>R</em> is a rank-one operator, <span> <span>(Vert T+RVert &gt;Vert TVert )</span> </span> but <span> <span>(T+R)</span> </span> does not attain its norm. This answers a question posed by Dantas and the first two authors. Furthermore, motivated by the parallelism exhibited in the literature between the <em>V</em>-property introduced by Khatskevich, Ostrovskii and Shulman and the weak maximizing property introduced by Aron, García, Pellegrino and Teixeira, we also study the relationship between these two properties and norm-attaining perturbations of operators.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"37 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140074236","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信