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Integral representation of balayage on locally compact spaces and its application
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-25 DOI: 10.1007/s13324-024-01007-9
Natalia Zorii
{"title":"Integral representation of balayage on locally compact spaces and its application","authors":"Natalia Zorii","doi":"10.1007/s13324-024-01007-9","DOIUrl":"10.1007/s13324-024-01007-9","url":null,"abstract":"<div><p>In the theory of inner and outer balayage of positive Radon measures on a locally compact space <i>X</i> to arbitrary <span>(Asubset X)</span> with respect to suitable, quite general function kernels, developed in a series of the author’s recent papers, we find conditions ensuring the validity of the integral representations. The results thereby obtained do hold and seem to be largely new even for several interesting kernels in classical and modern potential theory, which looks promising for possible applications. As an example of such applications, we analyze how the total mass of a measure varies under its balayage with respect to fractional Green kernels.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109577","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 variety of X-states
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-25 DOI: 10.1007/s13324-025-01010-8
Luca Candelori, Vladimir Y. Chernyak, John R. Klein
{"title":"On the variety of X-states","authors":"Luca Candelori,&nbsp;Vladimir Y. Chernyak,&nbsp;John R. Klein","doi":"10.1007/s13324-025-01010-8","DOIUrl":"10.1007/s13324-025-01010-8","url":null,"abstract":"<div><p>We introduce the notion of an X-state on <i>n</i>-qubits. After taking the Zariski closure of the set of X-states in the space of all mixed states, we obtain a complex algebraic variety <span>({mathscr {X}})</span> that is equipped with the action of the Lie group of local symmetries <i>G</i>. We show that the field of <i>G</i>-invariant rational functions on <span>({mathscr {X}})</span> is purely transcendental over the complex numbers of degree <span>(2^{2n-1}-n-1)</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109578","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
Multiple normalized solutions to critical Choquard equation involving fractional p-Laplacian in ({mathbb {R}}^{N})
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-25 DOI: 10.1007/s13324-025-01011-7
Xin Zhang, Thin Van Nguyen, Sihua Liang
{"title":"Multiple normalized solutions to critical Choquard equation involving fractional p-Laplacian in ({mathbb {R}}^{N})","authors":"Xin Zhang,&nbsp;Thin Van Nguyen,&nbsp;Sihua Liang","doi":"10.1007/s13324-025-01011-7","DOIUrl":"10.1007/s13324-025-01011-7","url":null,"abstract":"<div><p>The paper mainly investigates the existence of multiple normalized solutions for critical Choquard equation with involving fractional <i>p</i>-Laplacian in <span>({mathbb {R}}^{N})</span>: </p><div><div><span>$$begin{aligned} left{ ! begin{array}{lll} (-Delta )_{p}^{s}u !+!Z(kappa x)|u|^{p-2}u!=!lambda |u|^{p-2}u!+! Big [dfrac{1}{|x|^{N-alpha }}*|u|^{q}!Big ]|u|^{q-2}u!+!sigma |u|^{p_{s}^{*}-2}u &amp; text{ in } {mathbb {R}}^{N}!, displaystyle int _{{mathbb {R}}^{N}}|u|^{p}dx=a^{p}, end{array} right. end{aligned}$$</span></div></div><p>where <span>(kappa &gt; 0)</span> is a small parameter, <span>(lambda in {mathbb {R}})</span> is a Lagrange multiplier, <span>(Z:{mathbb {R}}^{N}rightarrow [0,infty ))</span> is a continuous function. Under the right conditions, together with the minimization techniques, truncated method, variational methods and the Lusternik–Schnirelmann category, we obtain the existence of multiple normalized solutions, which can be viewed as a partial extension of the previous results concerning the existence of normalized solutions to this problem in the case of <span>(s = 1)</span>, <span>(p = 2)</span> and subcritical case.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109582","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
Endpoint regularity of general Fourier integral operators
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-24 DOI: 10.1007/s13324-025-01013-5
Wenjuan Li, Xiangrong Zhu
{"title":"Endpoint regularity of general Fourier integral operators","authors":"Wenjuan Li,&nbsp;Xiangrong Zhu","doi":"10.1007/s13324-025-01013-5","DOIUrl":"10.1007/s13324-025-01013-5","url":null,"abstract":"<div><p>Let <span>(nge 1,0&lt;rho &lt;1, max {rho ,1-rho }le delta le 1)</span> and </p><div><div><span>$$begin{aligned} m_1=rho -n+(n-1)min {frac{1}{2},rho }+frac{1-delta }{2}. end{aligned}$$</span></div></div><p>If the amplitude <i>a</i> belongs to the Hörmander class <span>(S^{m_1}_{rho ,delta })</span> and <span>(phi in Phi ^{2})</span> satisfies the strong non-degeneracy condition, then we prove that the following Fourier integral operator <span>(T_{phi ,a})</span> defined by </p><div><div><span>$$begin{aligned} T_{phi ,a}f(x)=int _{{mathbb {R}}^{n}}e^{iphi (x,xi )}a(x,xi ){widehat{f}}(xi )dxi , end{aligned}$$</span></div></div><p>is bounded from the local Hardy space <span>(h^1({mathbb {R}}^n))</span> to <span>(L^1({mathbb {R}}^n))</span>. As a corollary, we can also obtain the corresponding <span>(L^p({mathbb {R}}^n))</span>-boundedness when <span>(1&lt;p&lt;2)</span>. These theorems are rigorous improvements on the recent works of Staubach and his collaborators. When <span>(0le rho le 1,delta le max {rho ,1-rho })</span>, by using some similar techniques in this note, we can get the corresponding theorems which coincide with the known results.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109320","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
Fractional integral operators in variable exponent Stummel spaces 变指数Stummel空间中的分数阶积分算子
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-15 DOI: 10.1007/s13324-024-01006-w
Alexandre Almeida, Humberto Rafeiro
{"title":"Fractional integral operators in variable exponent Stummel spaces","authors":"Alexandre Almeida,&nbsp;Humberto Rafeiro","doi":"10.1007/s13324-024-01006-w","DOIUrl":"10.1007/s13324-024-01006-w","url":null,"abstract":"<div><p>We prove the boundedness of the fractional maximal operator and the Riesz potential operator on variable exponent Stummel spaces. The main results rely on refined uniform weighted inequalities involving special weights with non-standard growth.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994592","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 limits of the Lie product formula type in Banach algebras Banach代数中李积公式类型的新极限
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-14 DOI: 10.1007/s13324-024-01002-0
Dumitru Popa
{"title":"New limits of the Lie product formula type in Banach algebras","authors":"Dumitru Popa","doi":"10.1007/s13324-024-01002-0","DOIUrl":"10.1007/s13324-024-01002-0","url":null,"abstract":"<div><p>We find new limits of the Lie product formula type in Banach algebras with unit. Some sample results: Let <i>X</i>, <i>Y</i>, <i>Z</i> be Banach algebras with unit, <span>( left( x_{n},y_{n}right) _{nin mathbb {N}}subset Xtimes Y)</span> convergent sequences with <span>(lim nolimits _{nrightarrow infty }x_{n}=x)</span>, <span>( lim nolimits _{nrightarrow infty }y_{n}=y)</span> and <span>(T:Xtimes Yrightarrow Z)</span> a continuous bilinear operator with <span>(Tleft( textbf{1},textbf{1}right) = textbf{1})</span>. Then for all sequences of natural numbers <span>(left( a_{n}right) _{nin mathbb {N}})</span> with <span>(lim nolimits _{nrightarrow infty }a_{n}=infty )</span> we have </p><div><div><span>$$begin{aligned} lim limits _{nrightarrow infty }left[ Tleft( prod limits _{k=1}^{n}e^{ frac{x_{k}}{a_{n}left( k+nright) left( k+2nright) }},prod limits _{k=1}^{n}e^{frac{y_{k}}{a_{n}left( k+2nright) left( k+3nright) } }right) right] ^{a_{n}}=e^{left( ln frac{4}{3}right) Tleft( x,textbf{ 1}right) +left( ln 2right) Tleft( textbf{1},yright) }; end{aligned}$$</span></div></div><div><div><span>$$begin{aligned} lim limits _{nrightarrow infty }left[ Tleft( prod limits _{k=1}^{n}cos frac{x_{k}}{a_{n}sqrt{nleft( n+kright) }},prod limits _{k=1}^{n}cos frac{ky_{k}}{na_{n}sqrt{n^{2}+k^{2}}}right) right] ^{na_{n}^{2}} end{aligned}$$</span></div></div><div><div><span>$$begin{aligned} =e^{-frac{left( ln 2right) Tleft( x^{2},textbf{1}right) +left( 1- frac{pi }{4}right) Tleft( textbf{1},y^{2}right) }{2}}. end{aligned}$$</span></div></div></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-01002-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976575","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
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
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