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Conformal structures with (G_2)-symmetric twistor distribution 具有（G_2）不对称扭曲分布的共形结构
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-03 DOI: 10.1007/s13324-025-01039-9
Pawel Nurowski, Katja Sagerschnig, Dennis The
{"title":"Conformal structures with (G_2)-symmetric twistor distribution","authors":"Pawel Nurowski,&nbsp;Katja Sagerschnig,&nbsp;Dennis The","doi":"10.1007/s13324-025-01039-9","DOIUrl":"10.1007/s13324-025-01039-9","url":null,"abstract":"<div><p>For any 4D split-signature conformal structure, there is an induced twistor distribution on the 5D space of all self-dual totally null 2-planes, which is (2, 3, 5) when the conformal structure is not anti-self-dual. Several examples where the twistor distribution achieves maximal symmetry (the split-real form of the exceptional simple Lie algebra of type <span>(textrm{G}_2)</span>) were previously known, and these include fascinating examples arising from the rolling of surfaces without twisting or slipping. We establish a complete local classification result for achieving maximal symmetry of the twistor distribution, identified among those homogeneous 4D split-conformal structures for which the conformal symmetry algebra induces a multiply-transitive action on the 5D space. Furthermore, we discuss geometric properties of these conformal structures such as their curvature, holonomy, and existence of Einstein representatives.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01039-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761764","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
Geometry and topology of spin random fields
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-21 DOI: 10.1007/s13324-025-01046-w
Antonio Lerario, Domenico Marinucci, Maurizia Rossi, Michele Stecconi
{"title":"Geometry and topology of spin random fields","authors":"Antonio Lerario,&nbsp;Domenico Marinucci,&nbsp;Maurizia Rossi,&nbsp;Michele Stecconi","doi":"10.1007/s13324-025-01046-w","DOIUrl":"10.1007/s13324-025-01046-w","url":null,"abstract":"<div><p>Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the Cosmic Microwave Background radiation. These objects can be viewed as random sections of the <i>s</i>-th complex tensor power of the tangent bundle of the 2-sphere. In this paper, we discuss how to characterize their expected geometry and topology. In particular, we investigate the asymptotic behaviour, under scaling assumptions, of general classes of geometric and topological functionals including Lipschitz–Killing Curvatures and Betti numbers for (properly defined) excursion sets; we cover both the cases of fixed and diverging spin parameters <i>s</i>. In the special case of monochromatic fields (i.e., spin random eigenfunctions) our results are particularly explicit; we show how their asymptotic behaviour is non-universal and we can obtain in particular complex versions of Berry’s random waves and of Bargmann–Fock’s models as subcases of a new generalized model, depending on the rate of divergence of the spin parameter <i>s</i>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667985","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
Binomial summation formulas involving Pell and Pell–Lucas polynomials
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-14 DOI: 10.1007/s13324-025-01045-x
Yulei Chen, Yanan Zhao, Dongwei Guo
{"title":"Binomial summation formulas involving Pell and Pell–Lucas polynomials","authors":"Yulei Chen,&nbsp;Yanan Zhao,&nbsp;Dongwei Guo","doi":"10.1007/s13324-025-01045-x","DOIUrl":"10.1007/s13324-025-01045-x","url":null,"abstract":"<div><p>By employing two fundamental binomial transformation formulae, several binomial summation formulas involving Pell and Pell-Lucas polynomials are established. Notably, specific instances of these formulas yield intriguing identities involving Fibonacci/Lucas and Pell/Pell-Lucas numbers. In particular, this work offers innovative proofs for two identities introduced by Ohtsuka and Tauraso (2020), as well as a problem posed by Seiffert in 1995.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621775","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
Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in ( {mathbf {mathbb {R}}}^{3} )
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-13 DOI: 10.1007/s13324-025-01044-y
Chandni Thakkar
{"title":"Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in ( {mathbf {mathbb {R}}}^{3} )","authors":"Chandni Thakkar","doi":"10.1007/s13324-025-01044-y","DOIUrl":"10.1007/s13324-025-01044-y","url":null,"abstract":"<div><p>In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is restricted over lines passing through a fixed curve <span>(gamma )</span> in <span>(mathbb {R}^3)</span> satisfying certain geometric conditions. The main theorem of the article shows that a second-order tensor field can be recovered from its restricted mixed-ray transform up to the kernel of the transform, a smoothing term, and a known singular term.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143602322","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 existence and prolongation of infinitesimal isometries on special sub-Riemannian manifolds
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-06 DOI: 10.1007/s13324-025-01035-z
Marek Grochowski
{"title":"On the existence and prolongation of infinitesimal isometries on special sub-Riemannian manifolds","authors":"Marek Grochowski","doi":"10.1007/s13324-025-01035-z","DOIUrl":"10.1007/s13324-025-01035-z","url":null,"abstract":"<div><p>In the present paper we deal with (local) infinitesimal isometries of special sub-Riemannian manifolds (a contact and oriented sub-Riemannian manifold is called special if the Reeb vector field is an infinitesimal isometry). The objective of the paper is to find some conditions on such manifolds which allow one to construct, locally around a given point, infinitesimal isometries and then, if possible, to prolong them onto bigger domains. The mentioned conditions are related to the so-called <span>(mathfrak {i}^*)</span>-regular and <span>(mathfrak {i})</span>-regular points, the notions introduced by Nomizu (Ann Math 2:105–120, 1960) in the Riemannian setting and slightly modified by the author.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553781","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
Characterizations of commutators of the maximal function in total Morrey spaces on stratified Lie groups
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-06 DOI: 10.1007/s13324-025-01038-w
Vagif S. Guliyev
{"title":"Characterizations of commutators of the maximal function in total Morrey spaces on stratified Lie groups","authors":"Vagif S. Guliyev","doi":"10.1007/s13324-025-01038-w","DOIUrl":"10.1007/s13324-025-01038-w","url":null,"abstract":"<div><p>The aim of this paper is to study the maximal commutators <span>(M_{b})</span> and the commutators of the maximal operator [<i>b</i>, <i>M</i>] in the total Morrey spaces <span>(L^{p,lambda ,mu }(mathbb {G}))</span> on any stratified Lie group <span>(mathbb {G})</span> when <i>b</i> belongs to Lipschitz spaces <span>({dot{Lambda }}_{beta }(mathbb {G}))</span>. Some new characterizations for certain subclasses of Lipschitz spaces <span>({dot{Lambda }}_{beta }(mathbb {G}))</span> are given.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553782","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
Weighted norm inequalities with one-dimensional Hardy-type operators involving suprema
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-06 DOI: 10.1007/s13324-025-01041-1
Vladimir D. Stepanov
{"title":"Weighted norm inequalities with one-dimensional Hardy-type operators involving suprema","authors":"Vladimir D. Stepanov","doi":"10.1007/s13324-025-01041-1","DOIUrl":"10.1007/s13324-025-01041-1","url":null,"abstract":"<div><p>In this paper we obtain necessary and sufficient conditions for the boundedness in weighted Lebesgue spaces of one-dimensional Hardy-type operators involving suprema. In particular, we solve the problems from Frank RL (J. Math. Sci. 263:323-342, 2022)</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564453","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 solutions of some nonlocal models for nonlinear dispersive waves
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-06 DOI: 10.1007/s13324-025-01042-0
Ailton C. Nascimento
{"title":"On the solutions of some nonlocal models for nonlinear dispersive waves","authors":"Ailton C. Nascimento","doi":"10.1007/s13324-025-01042-0","DOIUrl":"10.1007/s13324-025-01042-0","url":null,"abstract":"<div><p>In this paper we study special properties of solutions of the initial value problem associated to a class of nonlinear dispersive equations where the operator modelling dispersive effects is nonlocal. In particular, we prove that solutions of the surface tension Whitham equations posed on the real line satisfy the propagation of regularity phenomena, which says that regularity of the initial data on the right hand side of the real line is propagated to the left hand side by the flow solution. A similar result is obtained for solutions of the Full Dispersion Kadomtsev–Petviashvili equation, a natural (weakly transverse) two-dimensional version of the Whitham equation, with and without surface tension. We establish that the augmented regularity of the initial data on certain distinguished subsets of the Euclidean space is transmitted by the flow solution at an infinite rate. The underlying approach involves treating the general equation as a perturbed version of a class of fractional equations with well-established properties.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564454","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
Zygmund theorem for harmonic quasiregular mappings
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-05 DOI: 10.1007/s13324-025-01043-z
David Kalaj
{"title":"Zygmund theorem for harmonic quasiregular mappings","authors":"David Kalaj","doi":"10.1007/s13324-025-01043-z","DOIUrl":"10.1007/s13324-025-01043-z","url":null,"abstract":"<div><p>Let <span>(Kge 1)</span>. We prove Zygmund theorem for <span>(K-)</span>quasiregular harmonic mappings in the unit disk <span>(mathbb {D})</span> in the complex plane by providing a constant <i>C</i>(<i>K</i>) in the inequality </p><div><div><span>$$begin{aligned} Vert fVert _{1}le C(K)(1+Vert textrm{Re},(f)log ^+ |textrm{Re}, f|Vert _1), end{aligned}$$</span></div></div><p>provided that <span>(textrm{Im},f(0)=0)</span>. Moreover for a quasiregular harmonic mapping <span>(f=(f_1,dots , f_n))</span> defined in the unit ball <span>(mathbb {B}subset mathbb {R}^n)</span>, we prove the asymptotically sharp inequality </p><div><div><span>$$begin{aligned} Vert fVert _{1}-|f(0)|le (n-1)K^2(Vert f_1log f_1Vert _1- f_1(0)log f_1(0)), end{aligned}$$</span></div></div><p>when <span>(Krightarrow 1)</span>, provided that <span>(f_1)</span> is positive.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553937","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
Mixed radial-angular integrabilities for commutators of fractional Hardy operators with rough kernels 具有粗糙核的分数哈代算子换元的混合径向-角向积分性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-27 DOI: 10.1007/s13324-025-01037-x
Ronghui Liu, Shuangping Tao, Huoxiong Wu
{"title":"Mixed radial-angular integrabilities for commutators of fractional Hardy operators with rough kernels","authors":"Ronghui Liu,&nbsp;Shuangping Tao,&nbsp;Huoxiong Wu","doi":"10.1007/s13324-025-01037-x","DOIUrl":"10.1007/s13324-025-01037-x","url":null,"abstract":"<div><p>This paper is devoted to studying the boundedness of commutators <span>(textrm{H}_{Omega ,beta }^b)</span> generated by the rough fractional Hardy operators <span>(textrm{H}_{Omega ,beta })</span> with the symbol <i>b</i> on the mixed radial-angular spaces. When <i>b</i> is a mixed radial-angular central bounded mean oscillation function and <span>(Omega in L^s(S^{n-1}))</span> for some <span>(s&gt;1)</span>, the boundedness of <span>(textrm{H}_{Omega ,beta }^b)</span> on the mixed radial-angular homogeneous Herz spaces is established. Meanwhile, the boundedness for <span>(textrm{H}_{Omega ,beta }^b)</span> on the mixed radial-angular homogeneous <span>(lambda )</span>-central Morrey spaces is also obtained, provided that <i>b</i> belongs to the mixed radial-angular homogeneous <span>(lambda )</span>-central bounded mean oscillation spaces and <span>(Omega in L^s(S^{n-1}))</span> for some <span>(s&gt;1)</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513230","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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