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Modulus estimates of semirings with applications to boundary extension problems
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-31 DOI: 10.1007/s13324-025-01019-z
Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen
{"title":"Modulus estimates of semirings with applications to boundary extension problems","authors":"Anatoly Golberg,&nbsp;Toshiyuki Sugawa,&nbsp;Matti Vuorinen","doi":"10.1007/s13324-025-01019-z","DOIUrl":"10.1007/s13324-025-01019-z","url":null,"abstract":"<div><p>In our previous paper (Golberg et al. in Comput Methods Funct Theory 20(3–4):539–558, 2020), we proved that the complementary components of a ring domain in <span>(mathbb {R}^n)</span> with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems under quasiconformal mappings. In the present paper, we continue this work and investigate boundary extension problems for a larger class of mappings.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01019-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110078","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
Fibering polarizations and Mabuchi rays on symmetric spaces of compact type
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-29 DOI: 10.1007/s13324-025-01012-6
Thomas Baier, Ana Cristina Ferreira, Joachim Hilgert, José M. Mourão, João P. Nunes
{"title":"Fibering polarizations and Mabuchi rays on symmetric spaces of compact type","authors":"Thomas Baier,&nbsp;Ana Cristina Ferreira,&nbsp;Joachim Hilgert,&nbsp;José M. Mourão,&nbsp;João P. Nunes","doi":"10.1007/s13324-025-01012-6","DOIUrl":"10.1007/s13324-025-01012-6","url":null,"abstract":"<div><p>In this paper, we describe holomorphic quantizations of the cotangent bundle of a symmetric space of compact type <span>(T^*(U/K)cong U_mathbb {C}/K_mathbb {C})</span>, along Mabuchi rays of <i>U</i>-invariant Kähler structures. At infinite geodesic time, the Kähler polarizations converge to a mixed polarization <span>(mathcal {P}_infty )</span>. We show how a generalized coherent state transform (gCST) relates the quantizations along the Mabuchi geodesics such that holomorphic sections converge, as geodesic time goes to infinity, to distributional <span>(mathcal {P}_infty )</span>-polarized sections. Unlike in the case of <span>(T^*(U))</span>, the gCST mapping from the Hilbert space of vertically polarized sections are not asymptotically unitary due to the appearance of representation dependent factors associated to the isotypical decomposition for the <i>U</i>-action . In agreement with the general program outlined by Baier, Hilgert, Kaya, Mourão and Nunes in Journal of Geometry and Physics, 2025, we also describe how the quantization in the limit polarization <span>(mathcal {P}_infty )</span> is given by the direct sum of the quantizations for all the symplectic reductions relative to the invariant torus action associated to the Hamiltonian action of <i>U</i>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110143","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 a fractional Kirchhoff system with logarithmic nonlinearities
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s13324-025-01017-1
Romulo D. Carlos, Victor C. de Oliveira, Leandro S. Tavares
{"title":"On a fractional Kirchhoff system with logarithmic nonlinearities","authors":"Romulo D. Carlos,&nbsp;Victor C. de Oliveira,&nbsp;Leandro S. Tavares","doi":"10.1007/s13324-025-01017-1","DOIUrl":"10.1007/s13324-025-01017-1","url":null,"abstract":"<div><p>In this paper, two results regarding the existence and multiplicity of ground state solutions for a fractional Kirchhoff-type system involving logarithmic nonlinearities are obtained via variational methods. The proposed problem is motivated by several mathematical models that arise, for example, in quantum mechanics, nuclear physics, quantum optics, transport and diffusion phenomena, effective quantum gravity, open quantum systems, the theory of superfluidity, and Bose–Einstein condensation. The first result provides the existence of a ground state solution for the proposed problem. Under a different set of hypotheses with respect to the first result, a second one is obtained, which provides the existence of at least two non-trivial ground state solutions.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109966","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
Energy bounds for weighted spherical codes and designs via linear programming
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s13324-024-01009-7
S. V. Borodachov, P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin, E. B. Saff, M. M. Stoyanova
{"title":"Energy bounds for weighted spherical codes and designs via linear programming","authors":"S. V. Borodachov,&nbsp;P. G. Boyvalenkov,&nbsp;P. D. Dragnev,&nbsp;D. P. Hardin,&nbsp;E. B. Saff,&nbsp;M. M. Stoyanova","doi":"10.1007/s13324-024-01009-7","DOIUrl":"10.1007/s13324-024-01009-7","url":null,"abstract":"<div><p>Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar – every attaining code is optimal with respect to a large class of potential functions (absolutely monotone), in the sense of Levenshtein – there is a bound for every weighted code, and in the sense of parameters (nodes and weights) – they are independent of the potential function. We derive a necessary condition for optimality (in the linear programming framework) of our lower bounds which is also shown to be sufficient when the potential is strictly absolutely monotone. Bounds are also obtained for the weighted energy of weighted spherical designs. We demonstrate our bounds for several previously studied weighted spherical codes.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109509","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
Existence and regularity of solutions to mixed fully nonlinear local and nonlocal sub-elliptic equation in the Heisenberg group
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s13324-025-01018-0
Priyank Oza, Jagmohan Tyagi
{"title":"Existence and regularity of solutions to mixed fully nonlinear local and nonlocal sub-elliptic equation in the Heisenberg group","authors":"Priyank Oza,&nbsp;Jagmohan Tyagi","doi":"10.1007/s13324-025-01018-0","DOIUrl":"10.1007/s13324-025-01018-0","url":null,"abstract":"<div><p>We establish the comparison principle, existence and regularity of solutions to the following problem concerning the mixed operator: </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} alpha mathcal {M}^+_{lambda ,Lambda }big (D^2_{mathbbm {H}^N,S}ubig )-beta (-Delta _{mathbbm {H}^N})^su=f &amp; text {in } ,{Omega }, u=g &amp; text {in } ,mathbbm {H}^Nsetminus Omega , end{array}right. } end{aligned}$$</span></div></div><p>where <span>(mathcal {M}_{lambda ,Lambda }^+)</span> is the Pucci’s extremal operator and <span>((-Delta _{mathbbm {H}^N})^s)</span> denotes the fractional sub-Laplacian on the Heisenberg group <span>(mathbbm {H}^N.)</span></p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109957","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 direct products of critical metrics for quadratic curvature functionals
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s13324-025-01016-2
S. Caeiro-Oliveira
{"title":"On direct products of critical metrics for quadratic curvature functionals","authors":"S. Caeiro-Oliveira","doi":"10.1007/s13324-025-01016-2","DOIUrl":"10.1007/s13324-025-01016-2","url":null,"abstract":"<div><p>We study metrics on product manifolds which are critical for some quadratic curvature functionals. As a consequence, we provide construction methods and new examples in arbitrary dimension.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109965","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
Parametric symplectic jet interpolation
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1007/s13324-025-01015-3
Rafael B. Andrist, Gaofeng Huang, Frank Kutzschebauch, Josua Schott
{"title":"Parametric symplectic jet interpolation","authors":"Rafael B. Andrist,&nbsp;Gaofeng Huang,&nbsp;Frank Kutzschebauch,&nbsp;Josua Schott","doi":"10.1007/s13324-025-01015-3","DOIUrl":"10.1007/s13324-025-01015-3","url":null,"abstract":"<div><p>We prove a parametric jet interpolation theorem for symplectic holomorphic automorphisms of <span>(mathbb {C}^{2n})</span> with parameters in a Stein space. Moreover, we provide an example of an unavoidable set for symplectic holomorphic maps.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01015-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109688","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
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
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