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Kleinecke–Shirokov theorem: a version for isometric transformations 克莱涅克-希罗科夫定理：等距变换的版本
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-13 DOI: 10.1007/s13324-025-01057-7
Hranislav Stanković
{"title":"Kleinecke–Shirokov theorem: a version for isometric transformations","authors":"Hranislav Stanković","doi":"10.1007/s13324-025-01057-7","DOIUrl":"10.1007/s13324-025-01057-7","url":null,"abstract":"<div><p>In this paper, we present a version of the Kleinecke–Shirokov Theorem applicable to isometries on a Hilbert space <span>({mathcal {H}})</span>. Specifically, we demonstrate that if <span>( V in {mathfrak {B}}({mathcal {H}}))</span> is a quasinormal partial isometry and <span>(T in {mathfrak {B}}({mathcal {H}}))</span> satisfies <span>({mathcal {R}}(T) subseteq {mathcal {R}}(V))</span>, then </p><div><div><span>$$begin{aligned} [V,[V,T]]=0quad implies quad [V,T]=0. end{aligned}$$</span></div></div><p>We also consider the mixed commutators of two isometries, and their belonging to the Schatten-von Neumann classes. Finally, we show that the corresponding classical statement regarding normal operators can be derived from our results.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824617","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
Representation of real interpolation spaces using weighted couples of radon measures 用radon测度的加权偶表示实插值空间
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-10 DOI: 10.1007/s13324-025-01050-0
Per G. Nilsson
{"title":"Representation of real interpolation spaces using weighted couples of radon measures","authors":"Per G. Nilsson","doi":"10.1007/s13324-025-01050-0","DOIUrl":"10.1007/s13324-025-01050-0","url":null,"abstract":"<div><p>Using couples of weighted Radon measures an extension of the J-method of interpolation is described. This method allows for the representation also of non-regular interpolation spaces. In particular, Banach couples with the Calderon–Mitjagin property has all its interpolation spaces described by this extension.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818213","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
Long time behavior of solutions to the generalized Boussinesq equation 广义Boussinesq方程解的长时间行为
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-09 DOI: 10.1007/s13324-025-01048-8
Amin Esfahani, Gulcin M. Muslu
{"title":"Long time behavior of solutions to the generalized Boussinesq equation","authors":"Amin Esfahani,&nbsp;Gulcin M. Muslu","doi":"10.1007/s13324-025-01048-8","DOIUrl":"10.1007/s13324-025-01048-8","url":null,"abstract":"<div><p>In this paper, we investigate the generalized Boussinesq equation (gBq) as a model for the water wave problem with surface tension. Our study begins with the analysis of the initial value problem within Sobolev spaces, where we derive improved conditions for global existence and finite-time blow-up of solutions, extending previous results to lower Sobolev indices. Furthermore, we explore the time-decay behavior of solutions in Bessel potential and modulation spaces, establishing global well-posedness and time-decay estimates in these function spaces. Using Pohozaev-type identities, we demonstrate the non-existence of solitary waves for specific parameter regimes. A significant contribution of this work is the numerical generation of solitary wave solutions for the gBq equation using the Petviashvili iteration method. Additionally, we propose a Fourier pseudo-spectral numerical method to study the time evolution of solutions, particularly addressing the <i>gap interval</i> where theoretical results on global existence or blow-up are unavailable in the Sobolev spaces. Our numerical results provide new insights by confirming theoretical predictions in covered cases and filling gaps in unexplored scenarios. This comprehensive analysis not only clarifies the theoretical and numerical landscape of the gBq equation but also offers valuable tools for further investigations.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01048-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143801202","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
BC(_r): reductions of modified KP hierarchy BC (_r)：减少修改KP层次结构
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-06 DOI: 10.1007/s13324-025-01052-y
Haiyan Kang, Shen Wang, Jipeng Cheng
{"title":"BC(_r): reductions of modified KP hierarchy","authors":"Haiyan Kang,&nbsp;Shen Wang,&nbsp;Jipeng Cheng","doi":"10.1007/s13324-025-01052-y","DOIUrl":"10.1007/s13324-025-01052-y","url":null,"abstract":"<div><p>In this paper, one class of reductions of modified KP hierarchy is introduced, which is called the BC<span>(_r)</span>–modified KP hierarchy <span>((rge 0))</span> here, since it contains modified BKP and modified CKP hierarchies as special cases. For BC<span>(_r)</span>–modified KP hierarchy, we discuss Lax equations and bilinear descriptions, where the corresponding equivalence is also investigated.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143784227","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
General geronimus perturbations for mixed multiple orthogonal polynomials 混合多重正交多项式的一般格罗尼莫摄动
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-05 DOI: 10.1007/s13324-025-01036-y
Manuel Mañas, Miguel Rojas
{"title":"General geronimus perturbations for mixed multiple orthogonal polynomials","authors":"Manuel Mañas,&nbsp;Miguel Rojas","doi":"10.1007/s13324-025-01036-y","DOIUrl":"10.1007/s13324-025-01036-y","url":null,"abstract":"<div><p>General Geronimus transformations, defined by regular matrix polynomials that are neither required to be monic nor restricted by the rank of their leading coefficients, are applied through both right and left multiplication to a rectangular matrix of measures associated with mixed multiple orthogonal polynomials. These transformations produce Christoffel-type formulas that establish relationships between the perturbed and original polynomials. Moreover, it is proven that the existence of Geronimus-perturbed orthogonality is equivalent to the non-cancellation of certain <span>(tau )</span>-determinants. The effect of these transformations on the Markov–Stieltjes matrix functions is also determined. As a case study, we examine the Jacobi–Piñeiro orthogonal polynomials with three weights.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143784128","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
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 自旋随机场的几何和拓扑结构
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 涉及Pell和Pell - lucas多项式的二项式和公式
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} ) 二阶张量场的受限混合射线变换的微局部反演 ( {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 特殊次黎曼流形上无限小等距的存在性与扩展
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
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