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Mathematische Annalen最新文献

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Globally solvable time-periodic evolution equations in Gelfand–Shilov classes 格尔方-希洛夫类中全局可解的时周期演化方程
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-01 DOI: 10.1007/s00208-024-02925-6
Fernando de Ávila Silva, Marco Cappiello
{"title":"Globally solvable time-periodic evolution equations in Gelfand–Shilov classes","authors":"Fernando de Ávila Silva, Marco Cappiello","doi":"10.1007/s00208-024-02925-6","DOIUrl":"https://doi.org/10.1007/s00208-024-02925-6","url":null,"abstract":"<p>In this paper we consider a class of evolution operators with coefficients depending on time and space variables <span>((t,x) in {mathbb {T}}times {mathbb {R}}^n)</span>, where <span>({mathbb {T}})</span> is the one-dimensional torus, and prove necessary and sufficient conditions for their global solvability in (time-periodic) Gelfand–Shilov spaces. The argument of the proof is based on a characterization of these spaces in terms of the eigenfunction expansions given by a fixed self-adjoint, globally elliptic differential operator on <span>({mathbb {R}}^n)</span>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Factoring non-negative operator valued trigonometric polynomials in two variables 因式分解两变量中的非负算子值三角多项式
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-27 DOI: 10.1007/s00208-024-02895-9
Michael A. Dritschel
{"title":"Factoring non-negative operator valued trigonometric polynomials in two variables","authors":"Michael A. Dritschel","doi":"10.1007/s00208-024-02895-9","DOIUrl":"https://doi.org/10.1007/s00208-024-02895-9","url":null,"abstract":"<p>It is shown using Schur complement techniques that on dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree <span>((d_1,d_2))</span> can be written as a sum of hermitian squares of at most <span>(2d_2)</span> analytic polynomials.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"12 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Diagonals of self-adjoint operators II: non-compact operators 自相加算子的对角线 II：非紧凑算子
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-23 DOI: 10.1007/s00208-024-02910-z
Marcin Bownik, John Jasper
{"title":"Diagonals of self-adjoint operators II: non-compact operators","authors":"Marcin Bownik, John Jasper","doi":"10.1007/s00208-024-02910-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02910-z","url":null,"abstract":"<p>Given a self-adjoint operator <i>T</i> on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set <span>({mathcal {D}}(T))</span> of all possible diagonals of <i>T</i>. For operators <i>T</i> with at least two points in their essential spectrum <span>(sigma _{ess}(T))</span>, we give a complete characterization of <span>({mathcal {D}}(T))</span> for the class of self-adjoint operators sharing the same spectral measure as <i>T</i> with a possible exception of multiplicities of eigenvalues at the extreme points of <span>(sigma _{ess}(T))</span>. We also give a more precise description of <span>({mathcal {D}}(T))</span> for a fixed self-adjoint operator <i>T</i>, albeit modulo the kernel problem for special classes of operators. These classes consist of operators <i>T</i> for which an extreme point of the essential spectrum <span>(sigma _{ess}(T))</span> is also an extreme point of the spectrum <span>(sigma (T))</span>. Our results generalize a characterization of diagonals of orthogonal projections by Kadison [38, 39], Blaschke-type results of Müller and Tomilov [51] and Loreaux and Weiss [48], and a characterization of diagonals of operators with finite spectrum by the authors [15].</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"36 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Spectral moment formulae for $$GL(3)times GL(2)$$ L-functions III: the twisted case $$GL(3)/times GL(2)$$ L 函数的谱矩公式 III：扭曲情况
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-21 DOI: 10.1007/s00208-024-02914-9
Chung-Hang Kwan
{"title":"Spectral moment formulae for $$GL(3)times GL(2)$$ L-functions III: the twisted case","authors":"Chung-Hang Kwan","doi":"10.1007/s00208-024-02914-9","DOIUrl":"https://doi.org/10.1007/s00208-024-02914-9","url":null,"abstract":"<p>This is a sequel to our previous articles (Kwan in Algebra Number Theory. arXiv:2112.08568v4; Kwan in Spectral moment formulae for <span>(GL(3)times GL(2))</span> <i>L</i>-functions II: Eisenstein case, 2023. arXiv:2310.09419). In this work, we apply recent techniques that fall under the banner of ‘Period Reciprocity’ to study moments of <span>(GL(3)times GL(2))</span> <i>L</i>-functions in the non-archimedean aspects, with a view towards the ‘Twisted Moment Conjectures’ formulated by CFKRS.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"26 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Recognition of Seifert fibered spaces with boundary is in NP 有边界的塞弗特纤维空间的识别在 NP 中
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-20 DOI: 10.1007/s00208-024-02920-x
Adele Jackson
{"title":"Recognition of Seifert fibered spaces with boundary is in NP","authors":"Adele Jackson","doi":"10.1007/s00208-024-02920-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02920-x","url":null,"abstract":"<p>We show that the decision problem of recognising whether a triangulated 3-manifold admits a Seifert fibered structure with non-empty boundary is in NP. We also show that the problem of deciding whether a given triangulated Seifert fibered space with non-empty boundary admits certain Seifert data is in <span>({{{textbf {NP}}}{}}cap text {co-}{} {textbf {NP}})</span>. We do this by proving that in any triangulation of a Seifert fibered space with boundary there is both a fundamental horizontal surface of small degree and a complete collection of normal vertical annuli whose total weight is bounded by an exponential in the square of the triangulation size.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"23 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Global existence of entropy solutions for euler equations of compressible fluid flow 可压缩流体流动欧拉方程熵解的全局存在性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-18 DOI: 10.1007/s00208-024-02922-9
Yun-guang Lu, Christian Klingenberg, Xiangxing Tao
{"title":"Global existence of entropy solutions for euler equations of compressible fluid flow","authors":"Yun-guang Lu, Christian Klingenberg, Xiangxing Tao","doi":"10.1007/s00208-024-02922-9","DOIUrl":"https://doi.org/10.1007/s00208-024-02922-9","url":null,"abstract":"<p>The main contribution of this paper is to provide a complete proof of the global weak entropy solution existence of the Cauchy problem for the Euler equations of one-dimensional compressible fluid flow and to correct the mistakes in the paper “Global weak solutions of the one-dimensional hydrodynamic model for semiconductors” (Math. Mod. Meth. Appl. Sci., 6(1993), 759–788). Our technique is the method of the artificial viscosity coupled with the theory of compensated compactness, where four families of Lax entropy-entropy flux pair are constructed by means of the classical Fuchsian equation.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"20 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Optimal Sobolev regularity of $$bar{partial }$$ on the Hartogs triangle 哈托格三角形上$$bar{partial }$$的最优索波列夫正则性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-18 DOI: 10.1007/s00208-024-02919-4
Yifei Pan, Yuan Zhang
{"title":"Optimal Sobolev regularity of $$bar{partial }$$ on the Hartogs triangle","authors":"Yifei Pan, Yuan Zhang","doi":"10.1007/s00208-024-02919-4","DOIUrl":"https://doi.org/10.1007/s00208-024-02919-4","url":null,"abstract":"<p>In this paper, we show that for each <span>(kin {mathbb {Z}}^+, p&gt;4)</span>, there exists a solution operator <span>({mathcal {T}}_k)</span> to the <span>(bar{partial })</span> problem on the Hartogs triangle that maintains the same <span>(W^{k, p})</span> regularity as that of the data. According to a Kerzman-type example, this operator provides solutions with the optimal Sobolev regularity.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"205 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Exotic surfaces 奇异的表面
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-17 DOI: 10.1007/s00208-024-02916-7
Javier Reyes, Giancarlo Urzúa
{"title":"Exotic surfaces","authors":"Javier Reyes, Giancarlo Urzúa","doi":"10.1007/s00208-024-02916-7","DOIUrl":"https://doi.org/10.1007/s00208-024-02916-7","url":null,"abstract":"<p>Although exotic blow-ups of the projective plane at <i>n</i> points have been constructed for every <span>(n ge 2)</span>, the only examples known by means of rational blowdowns satisfy <span>(n ge 5)</span>. It has been an intriguing problem whether it is possible to decrease <i>n</i>. In this paper, we construct the first exotic <span>({mathbb {C}}{mathbb {P}}^2 # 4 overline{{mathbb {C}}{mathbb {P}}^2})</span> with this technique. We also construct exotic <span>(3{mathbb {C}}{mathbb {P}}^2 # b^- overline{{mathbb {C}}{mathbb {P}}^2})</span> for <span>(b^-=9,8,7)</span>. All of them are minimal and symplectic, as they are produced from projective surfaces <i>W</i> with Wahl singularities and <span>(K_W)</span> big and nef. In more generality, we elaborate on the problem of finding exotic </p><span>$$begin{aligned} (2chi ({mathcal {O}}_W)-1) {mathbb {C}}{mathbb {P}}^2 # (10chi ({mathcal {O}}_W)-K^2_W-1) overline{{mathbb {C}}{mathbb {P}}^2} end{aligned}$$</span><p>from these Kollár–Shepherd-Barron–Alexeev surfaces <i>W</i>, obtaining explicit geometric obstructions on the corresponding configurations of rational curves.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"72 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces 塞雷代数、矩阵因式分解和超曲面的分类托雷里定理
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-17 DOI: 10.1007/s00208-024-02915-8
Xun Lin, Shizhuo Zhang
{"title":"Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces","authors":"Xun Lin, Shizhuo Zhang","doi":"10.1007/s00208-024-02915-8","DOIUrl":"https://doi.org/10.1007/s00208-024-02915-8","url":null,"abstract":"<p>Let <i>X</i> be a smooth Fano variety. We attach a bi-graded associative algebra <span>(textrm{HS}(mathcal {K}u(X))=bigoplus _{i,jin mathbb {Z}} textrm{Hom}(textrm{Id},S_{mathcal {K}u(X)}^{i}[j]))</span> to the Kuznetsov component <span>(mathcal {K}u(X))</span> whenever it is defined. Then we construct a natural sub-algebra of <span>(textrm{HS}(mathcal {K}u(X)))</span> when <i>X</i> is a Fano hypersurface and establish its relation with Jacobian ring <span>(textrm{Jac}(X))</span>. As an application, we prove a categorical Torelli theorem for Fano hypersurface <span>(Xsubset mathbb {P}^n(nge 2))</span> of degree <i>d</i> if <span>(textrm{gcd}((n+1),d)=1.)</span> In addition, we give a new proof of the main theorem [15, Theorem 1.2] using a similar idea.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"24 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Simultaneous extreme values of zeta and L-functions zeta 函数和 L 函数的同时极值
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-14 DOI: 10.1007/s00208-024-02892-y
Winston Heap, Junxian Li
{"title":"Simultaneous extreme values of zeta and L-functions","authors":"Winston Heap, Junxian Li","doi":"10.1007/s00208-024-02892-y","DOIUrl":"https://doi.org/10.1007/s00208-024-02892-y","url":null,"abstract":"<p>We show that distinct primitive <i>L</i>-functions can achieve extreme values <i>simultaneously</i> on the critical line. Our proof uses a modification of the resonance method and can be applied to establish simultaneous extreme central values of <i>L</i>-functions in families.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"69 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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