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Quaternionic Balakrishnan operator and related semigroup property 四元数Balakrishnan算子及相关半群性质
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-07 DOI: 10.1007/s10231-026-01664-6
Guangzhou Qin, Chao Wang, Jibin Li
{"title":"Quaternionic Balakrishnan operator and related semigroup property","authors":"Guangzhou Qin,&nbsp;Chao Wang,&nbsp;Jibin Li","doi":"10.1007/s10231-026-01664-6","DOIUrl":"10.1007/s10231-026-01664-6","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the notion of quaternionic Balakrishnan operator <span>(J^{alpha })</span> with the quaternionic power (<span>(alpha in {mathbb {H}})</span> and <span>(textrm{Re}(alpha )&gt;0)</span>) is introduced via quaternionic non-negative operator <i>T</i> and the inclusion relations of the domains and ranges of these two types of operators are demonstrated. The unique unified integral representation of <span>(J^{alpha })</span> is obtained through the slice Cauchy kernels and the slice regularity of the exponent mapping is proved. Further, the limits of <span>(J^{alpha }x)</span> as <span>(alpha rightarrow 0)</span> and <span>(alpha rightarrow 1)</span> are investigated under some fixed spherical sectors. By obtaining moment inequality, we prove that <span>(J^{alpha })</span> is a closable operator and introduce the power with base <i>T</i> and exponent <span>(alpha )</span> as the operator <span>(overline{J^{alpha }})</span>, then the integral representation of <span>(overline{J^{alpha }})</span> is given by the limit of <i>S</i>-resolvent operator of <span>(-T)</span>. Besides, the related integral expressions of <span>(J^{alpha })</span> are established via quaternionic semigroup when <span>(-T)</span> is the infinitesimal generator of an equibounded strongly continuous quaternionic semigroup. It is crucial to note that the fractional quaternionic operator set <span>({overline{J_{T}^{alpha }}:alpha in {mathbb {H}}^{+}})</span> has a nice semigroup property under the <span>(*)</span>-<i>product</i> we introduced under the noncommutative setting. In addition, for the space consisting of right linear bounded quaternionic operators with a Schauder basis, we also obtained the semigroup property for <span>(J^{alpha })</span> through introducing the <span>(star )</span>-<i>product</i>.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2047 - 2071"},"PeriodicalIF":0.9,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628544","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
Alexandrov–Fenchel type inequalities with convex weight in space forms 空间形式中具有凸权的Alexandrov-Fenchel型不等式
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-07 DOI: 10.1007/s10231-026-01663-7
Kwok-Kun Kwong, Yong Wei
{"title":"Alexandrov–Fenchel type inequalities with convex weight in space forms","authors":"Kwok-Kun Kwong,&nbsp;Yong Wei","doi":"10.1007/s10231-026-01663-7","DOIUrl":"10.1007/s10231-026-01663-7","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we derive new sharp weighted Alexandrov–Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend classical results by incorporating weights given by convex, non-decreasing positive functions, which are otherwise arbitrary. Our approach gives rise to a broad family of geometric inequalities, as each convex, non-decreasing function yields a corresponding inequality, providing considerable flexibility. In particular, our results unify and extend a number of classical unweighted inequalities and their weighted extensions across different geometric settings. Finally, as an application of the weighted inequalities derived in our work, we establish a sharp upper bound for the first non-zero eigenvalue of a class of differential operators associated with <i>k</i>-convex hypersurfaces in <span>(mathbb {R}^n)</span>.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2021 - 2046"},"PeriodicalIF":0.9,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628580","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
Cartan flat non-degenerate CR lie groups 平面非简并CR李群
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-03 DOI: 10.1007/s10231-025-01651-3
Keizo Hasegawa, Hisashi Kasuya
{"title":"Cartan flat non-degenerate CR lie groups","authors":"Keizo Hasegawa,&nbsp;Hisashi Kasuya","doi":"10.1007/s10231-025-01651-3","DOIUrl":"10.1007/s10231-025-01651-3","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper we determine all the simply connected non-degenerate CR Lie groups, which are flat with respect to the Cartan connection: in terms of associated Lie algebras, we assert that the only Cartan flat non-degenerate CR Lie algebras are <span>(boldsymbol{mathfrak {s}}{boldsymbol{mathfrak {u}}}(text {2}), boldsymbol{mathfrak {s}}{boldsymbol{mathfrak {l}}}(text {2},mathbb {R}), {boldsymbol{mathfrak {a}}}{boldsymbol{mathfrak {f}}}{boldsymbol{mathfrak {f}}}(mathbb {R}) oplus mathbb {R})</span>, and <span>({boldsymbol{mathfrak {h}}}_{text {2m+1}})</span> with its modifications, where <span>({boldsymbol{mathfrak {a}}}{boldsymbol{mathfrak {f}}}{boldsymbol{mathfrak {f}}}(mathbb {R}))</span> is the affine Lie algebra of dimension 2 and <span>({boldsymbol{mathfrak {h}}}_{text {2m+1}})</span> is the Heisenberg Lie algebra of dimension 2 m+1. Furthermore, we determine all the (flat and non-flat) non-degenerate CR structures on each of these Lie groups.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 3","pages":"1685 - 1703"},"PeriodicalIF":0.9,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148268632","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
New explicit CMC cylinders and same-lobed CMC multibubbletons 新的显式CMC圆柱体和同叶CMC多气泡
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-03 DOI: 10.1007/s10231-026-01656-6
Joseph Cho, Katrin Leschke, Yuta Ogata
{"title":"New explicit CMC cylinders and same-lobed CMC multibubbletons","authors":"Joseph Cho,&nbsp;Katrin Leschke,&nbsp;Yuta Ogata","doi":"10.1007/s10231-026-01656-6","DOIUrl":"10.1007/s10231-026-01656-6","url":null,"abstract":"<div><p>By considering Darboux transforms of Delaunay surfaces, we obtain explicit conformal parametrisations leading to an examination of the symmetry and non-embeddedness of Delaunay bubbletons. Moreover, using the Darboux transformation on a multiple cover, we obtain new CMC cylinders with dihedral symmetry, providing their conformal parametrisations. These new CMC cylinders can be used to prove the existence of closed same-lobed CMC multibubbletons by applying Bianchi permutability.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1799 - 1829"},"PeriodicalIF":0.9,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628504","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
New insights into Gleason parts for an algebra of holomorphic functions 对全纯函数代数的格里森部分的新见解
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-03 DOI: 10.1007/s10231-026-01658-4
Daniel Carando, Verónica Dimant, Jorge Tomás Rodríguez
{"title":"New insights into Gleason parts for an algebra of holomorphic functions","authors":"Daniel Carando,&nbsp;Verónica Dimant,&nbsp;Jorge Tomás Rodríguez","doi":"10.1007/s10231-026-01658-4","DOIUrl":"10.1007/s10231-026-01658-4","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the structure of the spectrum of the algebra of uniformly continuous holomorphic functions on the unit ball of <span>(ell _p)</span>. Our main focus is the relationship between Gleason parts and fibers. For every <span>(z in B_{ell _p})</span> with <span>(1&lt; p &lt; infty )</span>, we prove that the fiber over <i>z</i> contains <span>(2^{mathfrak {c}})</span> distinct Gleason parts. We also investigate some of the properties of these Gleason parts and show the existence of many strong boundary points in certain fibers. We then examine the case <span>(p = 1)</span>, where similar results on the abundance of Gleason parts within the fibers hold, although the arguments required are more involved. Our results extend and complete earlier work on the subject, providing answers to previously posed questions.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1851 - 1884"},"PeriodicalIF":0.9,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628503","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 class group of (D+E[![Gamma ^*]!] ) 的类组 (D+E[![Gamma ^*]!] )
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-03 DOI: 10.1007/s10231-026-01657-5
Ahmed Hamed
{"title":"On the class group of (D+E[![Gamma ^*]!] )","authors":"Ahmed Hamed","doi":"10.1007/s10231-026-01657-5","DOIUrl":"10.1007/s10231-026-01657-5","url":null,"abstract":"<div><p>In this paper, we study the class group structure of rings of the form <span>(D + E[![Gamma ^*]!] )</span>, where <span>(D subseteq E)</span> is an extension of integral domains and <span>(Gamma )</span> is a numerical semigroup. We examine the properties of <i>t</i>-invertible and <i>v</i>-invertible fractional ideals in these rings and investigate their relationship with the <i>t</i>-class group <span>(operatorname {Cl}_t(D))</span> of the base domain <i>D</i>. Our primary results establish that the natural mapping <span>(varphi : operatorname {Cl}_t(D) rightarrow operatorname {Cl}_t(D + E[![Gamma ^*]!] ))</span> is an injective homomorphism when <i>E</i> is a flat <i>D</i>-module, although it is not surjective in general. Furthermore, we provide a complete characterization of the <i>t</i>-invertible <i>t</i>-ideals of <span>(D + E[![Gamma ^*]!] )</span> extended (with nonzero trace) to <i>D</i>. Specifically, we show that if <i>E</i> is completely integrally closed and <span>(operatorname {qf}(D) subseteq E,)</span> then every <i>t</i>-invertible <i>t</i>-ideal <i>I</i> of <span>(D+E[![Gamma ^*]!] )</span> with nonzero trace in <i>D</i> can be expressed as <span>(I = uJ(D+E[![Gamma ^*]!] ),)</span> for some <span>(uin operatorname {qf}(D+E[![Gamma ^*]!] ),)</span> and a nonzero <i>t</i>-ideal <i>J</i> of <i>D</i>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1831 - 1850"},"PeriodicalIF":0.9,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628505","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 differential complex on a compact Lie group 紧李群上的微分复形
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-01-24 DOI: 10.1007/s10231-026-01659-3
Paulo L. Dattori da Silva, Fernanda M. Simão
{"title":"A differential complex on a compact Lie group","authors":"Paulo L. Dattori da Silva,&nbsp;Fernanda M. Simão","doi":"10.1007/s10231-026-01659-3","DOIUrl":"10.1007/s10231-026-01659-3","url":null,"abstract":"<div>\u0000 \u0000 <p>We characterize the global solvability, in each level of the complex, of a differential complex associate to an involutive system of real vector fields defined on the product of the <i>n</i>-dimensional torus and a compact Lie group. Also we compute the induced cohomology groups. Our results are linked to a certain algebraic condition.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1885 - 1910"},"PeriodicalIF":0.9,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01659-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628472","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
Existence of solutions to a double phase elliptic problems involving the Hardy potential 一类含Hardy势的双相椭圆型问题解的存在性
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-01-24 DOI: 10.1007/s10231-026-01660-w
Luigi Muglia, Giuseppe Riey
{"title":"Existence of solutions to a double phase elliptic problems involving the Hardy potential","authors":"Luigi Muglia,&nbsp;Giuseppe Riey","doi":"10.1007/s10231-026-01660-w","DOIUrl":"10.1007/s10231-026-01660-w","url":null,"abstract":"<div><p>We prove existence of solutions for an elliptic equation involving a double phase operator and a supercritical Hardy potential. The existence is ensured by the presence of a lower order term depending on the gradient of the solution.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1911 - 1937"},"PeriodicalIF":0.9,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628473","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
Lower bounds for the first eigenvalues of the biharmonic operators on Riemannian (sub)manifolds 黎曼流形上双调和算子第一特征值的下界
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-01-19 DOI: 10.1007/s10231-025-01654-0
Hezi Lin
{"title":"Lower bounds for the first eigenvalues of the biharmonic operators on Riemannian (sub)manifolds","authors":"Hezi Lin","doi":"10.1007/s10231-025-01654-0","DOIUrl":"10.1007/s10231-025-01654-0","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we first give some lower bound estimate for the first eigenvalues of buckling and clamped plate problems on a complete non-compact submanifold in a strong negatively curved space, under an integral pinching condition on the mean curvature. Secondly, we establish lower bounds for these eigenvalue problems on bounded domains of a Riemannian manifold with Ricci curvature bounded from below by a negative constant, in terms of the inradius and the mean curvature of its boundary.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1755 - 1767"},"PeriodicalIF":0.9,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628642","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
Harmonic Bergman spaces on locally finite trees 局部有限树上的调和Bergman空间
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-01-16 DOI: 10.1007/s10231-025-01652-2
Alessandro Ottazzi, Federico Santagati
{"title":"Harmonic Bergman spaces on locally finite trees","authors":"Alessandro Ottazzi,&nbsp;Federico Santagati","doi":"10.1007/s10231-025-01652-2","DOIUrl":"10.1007/s10231-025-01652-2","url":null,"abstract":"<div><p>We define the harmonic Bergman space on locally finite trees with respect to a suitable probabilistic Laplacian and a class of weighted flow measures. We characterise the corresponding Bergman projection and prove that it is bounded on <span>(L^p)</span> for every <span>(p&gt;1)</span>, and of weak type (1, 1). We also prove necessary and sufficient conditions for the <span>(L^p)</span>-boundedness of the extension of a class of Toeplitz-type operators.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1705 - 1729"},"PeriodicalIF":0.9,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01652-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628682","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
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