Annali di Matematica Pura ed Applicata最新文献

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An extension result for (LB)-spaces and the surjectivity of tensorized mappings (LB)空间的扩展结果和张量映射的可射性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-01-29 DOI: 10.1007/s10231-023-01420-0
Andreas Debrouwere, Lenny Neyt
{"title":"An extension result for (LB)-spaces and the surjectivity of tensorized mappings","authors":"Andreas Debrouwere,&nbsp;Lenny Neyt","doi":"10.1007/s10231-023-01420-0","DOIUrl":"10.1007/s10231-023-01420-0","url":null,"abstract":"<div><p>We study an extension problem for continuous linear maps in the setting of (<i>LB</i>)-spaces. More precisely, we characterize the pairs (<i>E</i>, <i>Z</i>), where <i>E</i> is a locally complete space with a fundamental sequence of bounded sets and <i>Z</i> is an (<i>LB</i>)-space, such that for every exact sequence of (<i>LB</i>)-spaces </p><div><div><img></div></div><p>the map </p><div><div><span>$$begin{aligned} L(Y,E) rightarrow L(X, E), ~ T mapsto T circ iota end{aligned}$$</span></div></div><p>is surjective, meaning that each continuous linear map <span>(X rightarrow E)</span> can be extended to a continuous linear map <span>(Y rightarrow E)</span> via <span>(iota )</span>, under some mild conditions on <i>E</i> or <i>Z</i> (e.g. one of them is nuclear). We use our extension result to obtain sufficient conditions for the surjectivity of tensorized maps between Fréchet-Schwartz spaces. As an application of the latter, we study vector-valued Eidelheit type problems. Our work is inspired by and extends results of Vogt [24].</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1753 - 1781"},"PeriodicalIF":1.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881522","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
Embedded complex curves in the affine plane 仿射平面中的嵌入复曲线
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-01-29 DOI: 10.1007/s10231-023-01418-8
Antonio Alarcón, Franc Forstnerič
{"title":"Embedded complex curves in the affine plane","authors":"Antonio Alarcón,&nbsp;Franc Forstnerič","doi":"10.1007/s10231-023-01418-8","DOIUrl":"10.1007/s10231-023-01418-8","url":null,"abstract":"<div><p>This paper brings several contributions to the classical Forster–Bell–Narasimhan conjecture and the Yang problem concerning the existence of proper, almost proper, and complete injective holomorphic immersions of open Riemann surfaces in the affine plane <span>(mathbb {C}^2)</span> satisfying interpolation and hitting conditions. We also show that every compact Riemann surface contains a Cantor set whose complement admits a proper holomorphic embedding in <span>(mathbb {C}^2)</span>, and every connected domain in <span>(mathbb {C}^2)</span> admits complete, everywhere dense, injectively immersed complex discs. The focal point of the paper is a lemma saying for every compact bordered Riemann surface, <i>M</i>, closed discrete subset <i>E</i> of <span>(mathring{M}=Msetminus bM)</span>, and compact subset <span>(Ksubset mathring{M}setminus E)</span> without holes in <span>(mathring{M})</span>, any <span>(mathscr {C}^1)</span> embedding <span>(f:Mhookrightarrow mathbb {C}^2)</span> which is holomorphic in <span>(mathring{M})</span> can be approximated uniformly on <i>K</i> by holomorphic embeddings <span>(F:Mhookrightarrow mathbb {C}^2)</span> which map <span>(Ecup bM)</span> out of a given ball and satisfy some interpolation conditions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1673 - 1701"},"PeriodicalIF":1.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01418-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Horofunctions and metric compactification of noncompact Hermitian symmetric spaces 非紧凑赫尔墨斯对称空间的荷函数和度量紧凑化
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-01-24 DOI: 10.1007/s10231-023-01419-7
Cho-Ho Chu, María Cueto-Avellaneda, Bas Lemmens
{"title":"Horofunctions and metric compactification of noncompact Hermitian symmetric spaces","authors":"Cho-Ho Chu,&nbsp;María Cueto-Avellaneda,&nbsp;Bas Lemmens","doi":"10.1007/s10231-023-01419-7","DOIUrl":"10.1007/s10231-023-01419-7","url":null,"abstract":"<div><p>Given a Hermitian symmetric space <i>M</i> of noncompact type, we show, among other things, that the metric compactification of <i>M</i> with respect to its Carathéodory distance is homeomorphic to a closed ball in its tangent space. We first give a complete description of the horofunctions in the compactification of <i>M</i> via the realisation of <i>M</i> as the open unit ball <i>D</i> of a Banach space <span>((V,Vert cdot Vert ))</span> equipped with a particular Jordan structure, called a <span>(textrm{JB}^*)</span>-triple. We identify the horofunctions in the metric compactification of <span>((V,Vert cdot Vert ))</span> and relate its geometry and global topology, via a homeomorphism, to the closed unit ball of the dual space <span>(V^*)</span>. Finally, we show that the exponential map <span>(exp _0 :V longrightarrow D)</span> at <span>(0in D)</span> extends to a homeomorphism between the metric compactifications of <span>((V,Vert cdot Vert ))</span> and <span>((D,rho ))</span>, preserving the geometric structure, where <span>(rho )</span> is the Carathéodory distance on <i>D</i>. Consequently, the metric compactification of <i>M</i> admits a concrete realisation as the closed dual unit ball of <span>((V,Vert cdot Vert ))</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1703 - 1751"},"PeriodicalIF":1.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882047","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
Uniform maximal Fourier restriction for convex curves 凸曲线的均匀最大傅立叶限制
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-01-18 DOI: 10.1007/s10231-023-01417-9
Marco Fraccaroli
{"title":"Uniform maximal Fourier restriction for convex curves","authors":"Marco Fraccaroli","doi":"10.1007/s10231-023-01417-9","DOIUrl":"10.1007/s10231-023-01417-9","url":null,"abstract":"<div><p>We extend the estimates for maximal Fourier restriction operators proved by Müller et al. (Rev Mat Iberoam 35:693–702, 2019) and Ramos (Proc Am Math Soc 148:1131–1138, 2020) to the case of arbitrary convex curves in the plane, with constants uniform in the curve. The improvement over Müller, Ricci, and Wright and Ramos is given by the removal of the <span>({mathcal {C}}^2)</span> regularity condition on the curve. This requires the choice of an appropriate measure for each curve, that is suggested by an affine invariant construction of Oberlin (Michigan Math J 51:13–26, 2003). As corollaries, we obtain a uniform Fourier restriction theorem for arbitrary convex curves and a result on the Lebesgue points of the Fourier transform on the curve.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1643 - 1671"},"PeriodicalIF":1.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139526743","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
Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians 具有完全可分解雅各比的非简单极化无常曲面和属 3 曲线
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-01-17 DOI: 10.1007/s10231-023-01415-x
Robert Auffarth, Paweł Borówka
{"title":"Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians","authors":"Robert Auffarth,&nbsp;Paweł Borówka","doi":"10.1007/s10231-023-01415-x","DOIUrl":"10.1007/s10231-023-01415-x","url":null,"abstract":"<div><p>We study the space of non-simple polarised abelian surfaces. Specifically, we describe for which pairs (<i>m</i>, <i>n</i>) the locus of polarised abelian surfaces of type (1, <i>d</i>) that contain two complementary elliptic curve of exponents <i>m</i>, <i>n</i>, denoted <span>(mathcal {E}_d(m,n))</span> is non-empty. We show that if <i>d</i> is square-free, the locus <span>(mathcal {E}_d(m,n))</span> is an irreducible surface (if non-empty). We also show that the loci <span>(mathcal {E}_d(d,d))</span> can have many components if <i>d</i> is an odd square. As an application, we show that for a genus 3 curve with a completely decomposable Jacobian (i.e. isogenous to a product of 3 elliptic curves) the degrees of complementary coverings <span>(f_i:Crightarrow E_i, i=1,2,3)</span> satisfy <span>({{,textrm{lcm},}}(deg (f_1),deg (f_2))={{,textrm{lcm},}}(deg (f_1),deg (f_3))={{,textrm{lcm},}}(deg (f_2),deg (f_3)))</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1587 - 1605"},"PeriodicalIF":1.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881605","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
Angular properties of a tetrahedron with an acute triangular base 锐角三角底四面体的角度特性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-01-10 DOI: 10.1007/s10231-023-01416-w
M. Q. Rieck
{"title":"Angular properties of a tetrahedron with an acute triangular base","authors":"M. Q. Rieck","doi":"10.1007/s10231-023-01416-w","DOIUrl":"10.1007/s10231-023-01416-w","url":null,"abstract":"<div><p>From a fixed acute triangular base <span>(Delta ABC)</span>, all possible tetrahedra in three-dimensional real space are considered. The possible angles at the additional vertex <i>P</i> are shown to be bounded by certain inequalities, mostly linear inequalities. Together, these inequalities provide fairly tight bounds on the possible angle combinations at <i>P</i>. Four sets of inequalities are used for this purpose, though the inequalities in the first set are rather trivial. The inequalities in the second set can be established quickly, but do not seem to be known. The third and fourth set of inequalities are proved by studying scalar and vector fields on toroids. The first three sets of inequalities are linear in the angles at <i>P</i>, but the last set involves cosines of these angles. A generalization of the last two sets of inequalities is also proved, using the Poincaré–Hopf Theorem. Extensive testing of these results has been done using Mathematica and C++. The C++ code for this is listed in an appendix. While it has been demonstrated that the inequalities bound the possible combinations of angles at <i>P</i>, the results also reveal that additional inequalities, in particular linear inequalities, exist that would provided tighter bounds.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1607 - 1642"},"PeriodicalIF":1.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440794","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
Spectral convergence of Neumann Laplacian perturbed by an infinite set of curved holes 受无限曲面孔集扰动的诺伊曼拉普拉斯函数的谱收敛性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-01-04 DOI: 10.1007/s10231-023-01414-y
Hong Hai Ly
{"title":"Spectral convergence of Neumann Laplacian perturbed by an infinite set of curved holes","authors":"Hong Hai Ly","doi":"10.1007/s10231-023-01414-y","DOIUrl":"10.1007/s10231-023-01414-y","url":null,"abstract":"<div><p>We propose the novel spectral properties of the Neumann Laplacian in a two-dimensional bounded domain perturbed by an infinite number of compact sets with zero Lebesgue measure, so-called curved holes. These holes consist of segments or parts of curves enclosed in small spheres such that the diameters of holes tend to zero as the number of holes approaches infinity. Specifically, we rigorously demonstrate that the spectrum of the Neumann Laplacian on the perturbed domain converges to that of the original operator on the domain without holes under specific geometric assumptions and an appropriate selection of hole sizes. Furthermore, we derive sophisticated estimates on the convergence rate in terms of operator norms and estimate the Hausdorff distance between the spectra of the Laplacians.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1569 - 1585"},"PeriodicalIF":1.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139386501","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 sharp multiplier theorem for solvable extensions of Heisenberg and related groups 海森堡群及相关群可解扩展的尖锐乘数定理
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-26 DOI: 10.1007/s10231-023-01405-z
Alessio Martini, Paweł Plewa
{"title":"A sharp multiplier theorem for solvable extensions of Heisenberg and related groups","authors":"Alessio Martini,&nbsp;Paweł Plewa","doi":"10.1007/s10231-023-01405-z","DOIUrl":"10.1007/s10231-023-01405-z","url":null,"abstract":"<div><p>Let <i>G</i> be the semidirect product <span>(N rtimes mathbb {R})</span>, where <i>N</i> is a stratified Lie group and <span>(mathbb {R})</span> acts on <i>N</i> via automorphic dilations. Homogeneous left-invariant sub-Laplacians on <i>N</i> and <span>(mathbb {R})</span> can be lifted to <i>G</i>, and their sum <span>(Delta )</span> is a left-invariant sub-Laplacian on <i>G</i>. In previous joint work of Ottazzi, Vallarino and the first-named author, a spectral multiplier theorem of Mihlin–Hörmander type was proved for <span>(Delta )</span>, showing that an operator of the form <span>(F(Delta ))</span> is of weak type (1, 1) and bounded on <span>(L^p(G))</span> for all <span>(p in (1,infty ))</span> provided <i>F</i> satisfies a scale-invariant smoothness condition of order <span>(s &gt; (Q+1)/2)</span>, where <i>Q</i> is the homogeneous dimension of <i>N</i>. Here we show that, if <i>N</i> is a group of Heisenberg type, or more generally a direct product of Métivier and abelian groups, then the smoothness condition can be pushed down to the sharp threshold <span>(s&gt;(d+1)/2)</span>, where <i>d</i> is the topological dimension of <i>N</i>. The proof is based on lifting to <i>G</i> weighted Plancherel estimates on <i>N</i> and exploits a relation between the functional calculi for <span>(Delta )</span> and analogous operators on semidirect extensions of Bessel–Kingman hypergroups.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1361 - 1408"},"PeriodicalIF":1.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053790","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
Remarks about the mean value property and some weighted Poincaré-type inequalities 关于均值性质和一些加权波恩卡莱式不等式的评论
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-24 DOI: 10.1007/s10231-023-01408-w
Giorgio Poggesi
{"title":"Remarks about the mean value property and some weighted Poincaré-type inequalities","authors":"Giorgio Poggesi","doi":"10.1007/s10231-023-01408-w","DOIUrl":"10.1007/s10231-023-01408-w","url":null,"abstract":"<div><p>We start providing a quantitative stability theorem for the rigidity of an overdetermined problem involving harmonic functions in a punctured domain. Our approach is inspired by and based on the proof of rigidity established in Enciso and Peralta-Salas (Nonlinear Anal 70(2):1080–1086, 2009), and reveals essential differences with respect to the stability results obtained in the literature for the classical overdetermined Serrin problem. Secondly, we provide new weighted Poincaré-type inequalities for vector fields. These are crucial tools for the study of the quantitative stability issue initiated in Poggesi (Soap bubbles and convex cones: optimal quantitative rigidity, 2022. arXiv:2211.09429) concerning a class of rigidity results involving mixed boundary value problems. Finally, we provide a mean value-type property and an associated weighted Poincaré-type inequality for harmonic functions in cones. A duality relation between this new mean value property and a partially overdetermined boundary value problem is discussed, providing an extension of a classical result obtained in Payne and Schaefer (Math Methods Appl Sci 11(6):805–819, 1989).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1443 - 1461"},"PeriodicalIF":1.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139350754","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
Holomorphic extension in holomorphic fiber bundles with (1, 0)-compactifiable fiber 具有(1, 0)可压缩纤维的全态纤维束中的全态扩展
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-23 DOI: 10.1007/s10231-023-01412-0
Sergey Feklistov
{"title":"Holomorphic extension in holomorphic fiber bundles with (1, 0)-compactifiable fiber","authors":"Sergey Feklistov","doi":"10.1007/s10231-023-01412-0","DOIUrl":"10.1007/s10231-023-01412-0","url":null,"abstract":"<div><p>We use the Leray spectral sequence for the sheaf cohomology groups with compact supports to obtain a vanishing result. The stalks of sheaves <span>(R^{bullet }phi _{!}mathcal {O})</span> for the structure sheaf <span>(mathcal {O})</span> on the total space of a holomorphic fiber bundle <span>(phi )</span> has canonical topology structures. Using the standard Čech argument we prove a density lemma for QDFS-topology on this stalks. In particular, we obtain a vanishing result for holomorphic fiber bundles with Stein fibers. Using Künnet formulas, properties of an inductive topology (with respect to the pair of spaces) on the stalks of the sheaf <span>(R^{1}phi _{!}mathcal {O})</span> and a cohomological criterion for the Hartogs phenomenon we obtain the main result on the Hartogs phenomenon for the total space of holomorphic fiber bundles with (1, 0)-compactifiable fibers.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1529 - 1552"},"PeriodicalIF":1.0,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881534","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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