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Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field on disks in the strong field limit 强磁场极限下圆盘上磁场恒定的狄利克雷拉普拉斯算子的特征值
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-10 DOI: 10.1007/s13324-024-01008-8
Matthias Baur, Timo Weidl
{"title":"Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field on disks in the strong field limit","authors":"Matthias Baur,&nbsp;Timo Weidl","doi":"10.1007/s13324-024-01008-8","DOIUrl":"10.1007/s13324-024-01008-8","url":null,"abstract":"<div><p>We consider the magnetic Dirichlet Laplacian with constant magnetic field on domains of finite measure. First, in the case of a disk, we prove that the eigenvalue branches with respect to the field strength behave asymptotically linear with an exponentially small remainder term as the field strength goes to infinity. We compute the asymptotic expression for this remainder term. Second, we show that for sufficiently large magnetic field strengths, the spectral bound corresponding to the Pólya conjecture for the non-magnetic Dirichlet Laplacian is violated up to a sharp excess factor which is independent of the domain.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-01008-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142941205","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
Unimodularity and invariant volume forms for Hamiltonian dynamics on coisotropic Poisson homogeneous spaces 同向同性泊松齐次空间上哈密顿动力学的单模性和不变体积形式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-08 DOI: 10.1007/s13324-024-01003-z
I. Gutierrez-Sagredo, D. Iglesias-Ponte, J. C. Marrero, E. Padrón
{"title":"Unimodularity and invariant volume forms for Hamiltonian dynamics on coisotropic Poisson homogeneous spaces","authors":"I. Gutierrez-Sagredo,&nbsp;D. Iglesias-Ponte,&nbsp;J. C. Marrero,&nbsp;E. Padrón","doi":"10.1007/s13324-024-01003-z","DOIUrl":"10.1007/s13324-024-01003-z","url":null,"abstract":"<div><p>In this paper, we introduce a notion of multiplicative unimodularity for a coisotropic Poisson homogeneous space. Then, we discuss the unimodularity and the multiplicative unimodularity for these spaces and the existence of an invariant volume form for explicit Hamiltonian systems on such spaces. Several interesting examples illustrating the theoretical results are also presented.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-01003-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142938986","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
Boundedness of solutions of Chern-Simons-Higgs systems involving the (Delta _{lambda })-Laplacian 涉及(Delta _{lambda }) -拉普拉斯算子的chen - simons - higgs系统解的有界性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-07 DOI: 10.1007/s13324-024-01004-y
Nguyen Van Biet, Anh Tuan Duong, Yen Thi Ngoc Ha
{"title":"Boundedness of solutions of Chern-Simons-Higgs systems involving the (Delta _{lambda })-Laplacian","authors":"Nguyen Van Biet,&nbsp;Anh Tuan Duong,&nbsp;Yen Thi Ngoc Ha","doi":"10.1007/s13324-024-01004-y","DOIUrl":"10.1007/s13324-024-01004-y","url":null,"abstract":"<div><p>The purpose of this paper is to study the boundedness of solutions of the Chern-Simons-Higgs equation </p><div><div><span>$$begin{aligned} partial _tw-Delta _{lambda } w = left| w right| ^2 left( beta ^2-left| w right| ^2right) w-frac{1}{2}left( beta ^2-left| w right| ^2 right) ^2w text{ in } mathbb {R}times mathbb {R}^N end{aligned}$$</span></div></div><p>and system </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} partial _t u -Delta _lambda u = u^2left( 1-u^2-gamma v^2right) u-frac{1}{2}left( 1-u^2-gamma v^2 right) ^2u &amp; text { in } mathbb {R}times mathbb {R}^N, partial _t v -Delta _lambda v = v^2left( 1-v^2-gamma u^2right) v-frac{1}{2}left( 1-v^2-gamma u^2 right) ^2v &amp; text { in }mathbb {R}times mathbb {R}^N, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(gamma &gt;0)</span>, <span>(beta )</span> is a bounded continuous function and <span>(Delta _{lambda })</span> is the strongly degenerate operator defined by </p><div><div><span>$$begin{aligned} Delta _{lambda }:=sum _{i=1}^N partial _{x_i}left( lambda _i^2partial _{x_i} right) . end{aligned}$$</span></div></div><p>Under some general hypotheses of <span>(lambda _i)</span>, we shall establish some boundedness properties of solutions of the equation and system above. Our result can be seen as an extension of that in [<i>Li, Yayun; Lei, Yutian, Boundedness for solutions of equations of the Chern-Simons-Higgs type. Appl. Math. Lett.88(2019), 8-12.</i>]. In addition, we provide a simple proof of the boundedness of solutions.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939138","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
Noether symmetries of test charges in the magnetic monopole field 磁单极子场中测试电荷的诺特对称性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-06 DOI: 10.1007/s13324-024-01005-x
César S. López-Monsalvo, Alberto Rubio-Ponce
{"title":"Noether symmetries of test charges in the magnetic monopole field","authors":"César S. López-Monsalvo,&nbsp;Alberto Rubio-Ponce","doi":"10.1007/s13324-024-01005-x","DOIUrl":"10.1007/s13324-024-01005-x","url":null,"abstract":"<div><p>We consider the motion of charged test particles in the presence of a Dirac magnetic monopole. We use an extension of Noether’s theorem for systems with magnetic forces and integrate explicitly the corresponding equations of motion.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-01005-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925566","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
On the Laplace operator with a weak magnetic field in exterior domains 外域弱磁场下的拉普拉斯算子
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-27 DOI: 10.1007/s13324-024-01001-1
Ayman Kachmar, Vladimir Lotoreichik, Mikael Sundqvist
{"title":"On the Laplace operator with a weak magnetic field in exterior domains","authors":"Ayman Kachmar,&nbsp;Vladimir Lotoreichik,&nbsp;Mikael Sundqvist","doi":"10.1007/s13324-024-01001-1","DOIUrl":"10.1007/s13324-024-01001-1","url":null,"abstract":"<div><p>We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate asymptotics of the low-lying eigenvalues in the weak magnetic field limit. For the exterior of a star-shaped domain, we obtain an asymptotic upper bound on the lowest eigenvalue in the weak field limit, involving the <span>(4)</span>-moment, and optimal for the case of the disk. Moreover, we prove that, for moderate magnetic fields, the exterior of the disk is a local maximizer for the lowest eigenvalue under a <span>(p)</span>-moment constraint.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889934","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
Riesz capacity: monotonicity, continuity, diameter and volume Riesz容量：单调性、连续性、直径和体积
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-19 DOI: 10.1007/s13324-024-01000-2
Carrie Clark, Richard S. Laugesen
{"title":"Riesz capacity: monotonicity, continuity, diameter and volume","authors":"Carrie Clark,&nbsp;Richard S. Laugesen","doi":"10.1007/s13324-024-01000-2","DOIUrl":"10.1007/s13324-024-01000-2","url":null,"abstract":"<div><p>Properties of Riesz capacity are developed with respect to the kernel exponent <span>(p in (-infty ,n))</span>, namely that capacity is strictly monotonic as a function of <i>p</i>, that its endpoint limits recover the diameter and volume of the set, and that capacity is left-continuous with respect to <i>p</i> and is right-continuous provided (when <span>(p ge 0)</span>) that an additional hypothesis holds. Left and right continuity properties of the equilibrium measure are obtained too.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859514","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
Balayage, equilibrium measure, and Deny’s principle of positivity of mass for (alpha )-Green potentials 平衡测量，以及(alpha ) -格林势的质量正性的否定原理
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-13 DOI: 10.1007/s13324-024-00995-y
Natalia Zorii
{"title":"Balayage, equilibrium measure, and Deny’s principle of positivity of mass for (alpha )-Green potentials","authors":"Natalia Zorii","doi":"10.1007/s13324-024-00995-y","DOIUrl":"10.1007/s13324-024-00995-y","url":null,"abstract":"<div><p>In the theory of <span>(g_alpha )</span>-potentials on a domain <span>(Dsubset mathbb R^n)</span>, <span>(ngeqslant 2)</span>, <span>(g_alpha )</span> being the <span>(alpha )</span>-Green kernel associated with the <span>(alpha )</span>-Riesz kernel <span>(|x-y|^{alpha -n})</span> of order <span>(alpha in (0,n))</span>, <span>(alpha leqslant 2)</span>, we establish the existence and uniqueness of the <span>(g_alpha )</span>-balayage <span>(mu ^F)</span> of a positive Radon measure <span>(mu )</span> onto a relatively closed set <span>(Fsubset D)</span>, we analyze its alternative characterizations, and we provide necessary and/or sufficient conditions for <span>(mu ^F(D)=mu (D))</span> to hold, given in terms of the <span>(alpha )</span>-harmonic measure of suitable Borel subsets of <span>(overline{mathbb R^n})</span>, the one-point compactification of <span>(mathbb R^n)</span>. As a by-product, we find necessary and/or sufficient conditions for the existence of the <span>(g_alpha )</span>-equilibrium measure <span>(gamma _F)</span>, <span>(gamma _F)</span> being understood in an extended sense where <span>(gamma _F(D))</span> might be infinite. We also discover quite a surprising version of Deny’s principle of positivity of mass for <span>(g_alpha )</span>-potentials, thereby significantly improving a previous result by Fuglede and Zorii (Ann Acad Sci Fenn Math 43:121–145, 2018). The results thus obtained are sharp, which is illustrated by means of a number of examples. Some open questions are also posed.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142810994","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
Old and new on the Peetre K-functional and its relations to real interpolation theory, quasi-monotone functions and wavelets 彼得k泛函的新与旧及其与实插值理论、拟单调函数和小波的关系
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-10 DOI: 10.1007/s13324-024-00998-9
Rune Dalmo, Lars-Erik Persson, Natasha Samko
{"title":"Old and new on the Peetre K-functional and its relations to real interpolation theory, quasi-monotone functions and wavelets","authors":"Rune Dalmo,&nbsp;Lars-Erik Persson,&nbsp;Natasha Samko","doi":"10.1007/s13324-024-00998-9","DOIUrl":"10.1007/s13324-024-00998-9","url":null,"abstract":"<div><p>The Peetre K-functional is a key object in the development of the real method of interpolation. In this paper we point out a less known relation to wavelet theory and its applications to approximation theory and engineering applications. As a new basis for further development of these studies we present some known properties in the form appropriate for further applications and then derive new information and prove some new results concerning the K-functional and its close relation to (almost) quasi-monotone functions, various indices and interpolation theory. In particular, we extend and unify some known function parameter generalizations of the standard real interpolation spaces <span>((A_0, A_1)_{theta ,q})</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00998-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798257","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
Questions in linear recurrence I: the (Toplus T)-recurrence problem 线性递归中的问题1:(Toplus T)递归问题
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-09 DOI: 10.1007/s13324-024-00999-8
Sophie Grivaux, Antoni López-Martínez, Alfred Peris
{"title":"Questions in linear recurrence I: the (Toplus T)-recurrence problem","authors":"Sophie Grivaux,&nbsp;Antoni López-Martínez,&nbsp;Alfred Peris","doi":"10.1007/s13324-024-00999-8","DOIUrl":"10.1007/s13324-024-00999-8","url":null,"abstract":"<div><p>We study, for a continuous linear operator <i>T</i> acting on an F-space <i>X</i>, when the direct sum operator <span>(Toplus T)</span> is recurrent on the direct sum space <span>(Xoplus X)</span>. In particular: we establish the analogous notion for recurrence to that of (topological) weak-mixing for transitivity/hypercyclicity, namely quasi-rigidity; and we construct a recurrent but not quasi-rigid operator on each separable infinite-dimensional Banach space, solving the <span>(Toplus T)</span>-recurrence problem in the negative way.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00999-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798436","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
Symmetrization process and truncated orthogonal polynomials 对称过程与截断正交多项式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-29 DOI: 10.1007/s13324-024-00974-3
Diego Dominici, Juan Carlos García-Ardila, Francisco Marcellán
{"title":"Symmetrization process and truncated orthogonal polynomials","authors":"Diego Dominici,&nbsp;Juan Carlos García-Ardila,&nbsp;Francisco Marcellán","doi":"10.1007/s13324-024-00974-3","DOIUrl":"10.1007/s13324-024-00974-3","url":null,"abstract":"<div><p>We define the family of truncated Laguerre polynomials <span>(P_n(x;z))</span>, orthogonal with respect to the linear functional <span>(varvec{ell })</span> defined by </p><div><div><span>$$begin{aligned} leftlangle {varvec{ell },p}rightrangle =int _{0}^zp(x)x^alpha e^{-x}dx,qquad alpha &gt;-1. end{aligned}$$</span></div></div><p>The connection between <span>(P_n(x;z))</span> and the polynomials <span>(S_n(x;z))</span> (obtained through the symmetrization process) constitutes a key element in our analysis. As a consequence, several properties of the polynomials <span>(P_n(x;z))</span> and <span>(S_n(x;z))</span> are studied taking into account the relation between the parameters of the three-term recurrence relations that they satisfy. Asymptotic expansions of these coefficients are given. Discrete Painlevé and Painlevé equations associated with such coefficients appear in a natural way. An electrostatic interpretation of the zeros of such polynomials as well as the dynamics of the zeros in terms of the parameter <i>z</i> are given.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00974-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142754025","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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