Analysis and Mathematical Physics最新文献

{"title":"Critical temperatures and collapsing of two-dimensional Log gases","authors":"Rolf Andreasson,&nbsp;Ludvig Svensson","doi":"10.1007/s13324-026-01283-7","DOIUrl":"10.1007/s13324-026-01283-7","url":null,"abstract":"<div><p>We consider the canonical ensemble of a system of point particles on the sphere interacting via a logarithmic pair potential. We study the behavior of the associated Gibbs measure as the inverse temperature approaches a critical value at which the partition function diverges. One of our main results shows that the Gibbs measure converges weakly to a probability measure supported on degenerate configurations in which certain subsets of particles collapse. We characterize the possible clusters in the limiting configurations in terms of the solutions of a discrete optimization problem, which also determines the critical inverse temperature. Our approach relies on the Fulton–MacPherson compactification of configuration spaces and meromorphic continuation of complex powers. For the two-component plasma with arbitrary charges, we solve the optimization problem explicitly and thereby obtain a complete description of the possible limiting clusters. In particular, the limiting measure is supported on configurations where a maximal number of positive–negative dipoles have formed. Allowing completely general charges is motivated in part by Onsager’s model of turbulence. In this context, we establish explicit probabilistic bounds for the critical inverse temperature in case of random coupling and charges, using general estimates expressed in terms of eigenvalues of the coupling matrix.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01283-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339547","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}

{"title":"Band spectrum singularities for Schrödinger operators","authors":"Alexis Drouot,&nbsp;Curtiss Lyman","doi":"10.1007/s13324-026-01275-7","DOIUrl":"10.1007/s13324-026-01275-7","url":null,"abstract":"<div><p>In this paper, we develop a systematic framework to study the dispersion surfaces of Schrödinger operators <span>( -Delta + V)</span>, where the potential <span>(V in C^infty ({mathbb {R}}^n,{mathbb {R}}))</span> is periodic with respect to a lattice <span>(Lambda subset {mathbb {R}}^n)</span> and respects the symmetries of <span>(Lambda )</span>. Our analysis combines the theory of holomorphic families of operators of type (A) with the seminal work of Fefferman–Weinstein [1]. It allows us to extend results on the existence of spectral degeneracies past a perturbative regime. As an application, we describe the generic structure of some singularities in the band spectrum of Schrödinger operators invariant under the three-dimensional simple, body-centered and face-centered cubic lattices.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339139","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}

{"title":"On the constrained Kadomtsev-Petviashvili hierarchy: additional symmetries and gauge transformations","authors":"Song Li,&nbsp;Kelei Tian","doi":"10.1007/s13324-026-01285-5","DOIUrl":"10.1007/s13324-026-01285-5","url":null,"abstract":"<div><p>In this paper, we study two constrained cases of the Kadomtsev-Petviashvili hierarchy, named the generalized constrained Kadomtsev-Petviashvili and the generalized constrained modified Kadomtsev-Petviashvili hierarchies. The additional symmetries and gauge transformations for the generalized constrained Kadomtsev-Petviashvili hierarchy are given. These flows form a subalgebra of the Virasoro algebra. We give explicit formulas for the action of the additional flows for the generalized constrained Kadomtsev-Petviashvili and the generalized constrained modified Kadomtsev-Petviashvili hierarchies on tau functions. The additional flows for the generalized constrained Kadomtsev-Petviashvili hierarchy commuted with gauge transformations preserve their original form, up to shifting of the additional flows by the sum of two squared eigenfunction symmetry flows.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149235002","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}

{"title":"Cut loci of Berger type Lorentzian structures","authors":"A. V. Podobryaev","doi":"10.1007/s13324-026-01278-4","DOIUrl":"10.1007/s13324-026-01278-4","url":null,"abstract":"<div><p>Consider the deformation of the standard Lorentzian metric on the anti de-Sitter space along the fibers of the Hopf fibration. We study the universal covering of this Lorentzian manifold to exclude a priori presence of time-like cycles. We describe the sets attainable by admissible curves and study the question of the existence of the longest arcs. Next, we investigate Lorentzian geodesics for optimality: we find the cut time and the cut locus. As a geometric application we compute the injectivity radius of the corresponding Lorentzian manifold.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234429","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}

{"title":"Quadratic & additive mappings on operator commuting elements in ({textrm{JBW}}^*)-algebras","authors":"Gerardo M. Escolano,&nbsp;Jan Hamhalter,&nbsp;Antonio M. Peralta,&nbsp;Armando R. Villena","doi":"10.1007/s13324-026-01277-5","DOIUrl":"10.1007/s13324-026-01277-5","url":null,"abstract":"&lt;div&gt;&lt;p&gt;Let &lt;span&gt;(mathfrak {A})&lt;/span&gt; and &lt;span&gt;(mathfrak {B})&lt;/span&gt; be &lt;span&gt;({textrm{JBW}}^*)&lt;/span&gt;-algebras whose sets of unitaries are denoted by &lt;span&gt;(mathscr {U}(mathfrak {A}))&lt;/span&gt; and &lt;span&gt;(mathscr {U}(mathfrak {B}))&lt;/span&gt;, respectively. We show that &lt;span&gt;(mathscr {U}(mathfrak {A}))&lt;/span&gt; is closed for Jordan products of operator commuting pairs inside itself. Let &lt;span&gt;(mathfrak {A})&lt;/span&gt; and &lt;span&gt;(mathfrak {B})&lt;/span&gt; be &lt;span&gt;({textrm{JBW}}^*)&lt;/span&gt;-algebras without direct summands of type &lt;span&gt;(I_1)&lt;/span&gt; or &lt;span&gt;(I_2)&lt;/span&gt;, and let &lt;span&gt;(Phi : mathscr {U}(mathfrak {A}) rightarrow mathscr {U}(mathfrak {B}))&lt;/span&gt; be a bicontinuous bijection satisfying &lt;span&gt;(Phi (u circ v) = Phi (u)circ Phi (v))&lt;/span&gt; whenever &lt;i&gt;u&lt;/i&gt; and &lt;i&gt;v&lt;/i&gt; are operator commuting unitaries in &lt;span&gt;(mathfrak {A})&lt;/span&gt;. We prove that there exist a linear Jordan &lt;span&gt;({phantom {a}}^*)&lt;/span&gt;-isomorphism &lt;span&gt;(theta : mathfrak {A} rightarrow mathfrak {B})&lt;/span&gt;, a real linear mapping &lt;span&gt;(beta : mathfrak {A_{sa}}rightarrow Z(mathfrak {B}_{sa}))&lt;/span&gt;, and an invertible central element &lt;span&gt;(c in mathfrak {B}_{sa})&lt;/span&gt; such that &lt;/p&gt;&lt;div&gt;&lt;div&gt;&lt;span&gt;$$begin{aligned} Phi (e^{i a}) = e^{i beta (a)}circ e^{i ccirc theta (a)} = e^{i beta (a)} circ theta left( e^{i theta ^{-1}( c )circ a}right) , end{aligned}$$&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;&lt;p&gt;for all &lt;span&gt;(ain mathfrak {A}_{sa})&lt;/span&gt;. The conclusion improves when &lt;span&gt;(mathfrak {A})&lt;/span&gt; is a &lt;span&gt;({textrm{JBW}}^*)&lt;/span&gt;-algebra factor not of type &lt;span&gt;(I_2)&lt;/span&gt;. Assuming that &lt;span&gt;(mathfrak {A})&lt;/span&gt; has no direct summands of type &lt;span&gt;(I_2)&lt;/span&gt;, we show that any mapping &lt;span&gt;(Phi : mathfrak {A}_{sa} rightarrow mathfrak {B}_{sa})&lt;/span&gt; satisfying the following conditions: &lt;/p&gt;&lt;ol&gt;\u0000 &lt;li&gt;\u0000 &lt;span&gt;(a)&lt;/span&gt;\u0000 \u0000 &lt;p&gt;&lt;span&gt;(Phi big (U_a(b)big ) = U_{Phi (a)}big (Phi (b)big ))&lt;/span&gt; whenever &lt;i&gt;a&lt;/i&gt; and &lt;i&gt;b&lt;/i&gt; operator commute in &lt;span&gt;(mathfrak {A}_{sa})&lt;/span&gt;,&lt;/p&gt;\u0000 \u0000 &lt;/li&gt;\u0000 &lt;li&gt;\u0000 &lt;span&gt;(b)&lt;/span&gt;\u0000 \u0000 &lt;p&gt;&lt;span&gt;(Phi )&lt;/span&gt; is additive on pairs of operator commuting elements,&lt;/p&gt;\u0000 \u0000 &lt;/li&gt;\u0000 &lt;/ol&gt;&lt;p&gt; enjoys the following properties: First, &lt;span&gt;(Phi (textbf{1}))&lt;/span&gt; is a tripotent in &lt;span&gt;(mathfrak {B}_{sa})&lt;/span&gt;, the Peirce-2 subspace &lt;span&gt;(mathfrak {B}_2!left( Phi (textbf{1})right) )&lt;/span&gt; carries a natural structure of &lt;span&gt;({textrm{JBW}}^*)&lt;/span&gt;-algebra whose self-adjoint part contains the range of &lt;span&gt;(Phi )&lt;/span&gt;, and makes the corresponding mapping &lt;span&gt;(Phi : mathfrak {A}_{sa} rightarrow mathfrak {B}_2!left( Phi (textbf{1})right) _{sa})&lt;/span&gt; a unital (real linear) Jordan homomorphism. Furthermore, if &lt;span&gt;(Phi )&lt;/span&gt; is bijective, then &lt;span&gt;(Phi (textbf{1}))&lt;/span&gt; is a central symmetry in &lt;span&gt;(mathfrak {B})&lt;/span&gt;, and &lt;span&gt;(Phi )&lt;/span&gt;","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189289","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}

{"title":"Flux-explicit Cheeger bounds for magnetic Laplacians on compact metric graphs","authors":"B. E. Dahlke","doi":"10.1007/s13324-026-01281-9","DOIUrl":"10.1007/s13324-026-01281-9","url":null,"abstract":"<div><p>Let <span>(Gamma )</span> be a finite compact connected metric graph and let <span>(Ain L^infty (Gamma ))</span> be a real magnetic potential. The magnetic Laplacian <span>(H_A)</span> with standard vertex conditions is defined by the closed quadratic form </p><div><div><span>$$ mathfrak q_A[u]=sum _{e}int _e |(-mathrm ipartial _x-A_e)u_e|^2,mathrm dx . $$</span></div></div><p>The frustration-index Cheeger framework of Lange, Liu, Peyerimhoff and Post is adapted to compact metric graphs. The principal result identifies the frustration index on every regular subdomain with a finite-dimensional <span>(ell ^1)</span> flux distance determined by the periods of <i>A</i> on cycles. Consequently the Cheeger constant can be written directly in terms of Aharonov–Bohm fluxes. We prove </p><div><div><span>$$ lambda _0(H_A)ge frac{1}{5},h_A(Gamma )^2, $$</span></div></div><p>where <span>(lambda _0(H_A))</span> is the bottom of the spectrum. In particular, if <span>(delta _Gamma (Phi ))</span> denotes the flux distance of the global cycle-flux vector from the integral flux lattice, then </p><div><div><span>$$ lambda _0(H_A)ge frac{1}{5} min left{ h_textrm{pr}(Gamma ),frac{delta _Gamma (Phi )}{|Gamma |}right} ^2 . $$</span></div></div><p>The corresponding heat-semigroup and magnetic-energy decay estimates follow from the spectral theorem. An upper bound with geometric dependence is also given, together with an example excluding a graph-independent upper bound by a constant multiple of <span>(h_A(Gamma )^2)</span>. The lower-bound constant is not asserted to be sharp.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189239","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}

{"title":"On Montel theorem for mappings with inverse moduli inequalities","authors":"Miodrag Mateljević,&nbsp;Evgeny Sevost’yanov","doi":"10.1007/s13324-026-01279-3","DOIUrl":"10.1007/s13324-026-01279-3","url":null,"abstract":"<div><p>This paper is devoted to the study of mappings with finite distortion, in particular, mappings satisfying the inverse Poletskii inequality. We study the problem of equicontinuity of families of such mappings in a given domain. We establish that a family of open discrete mappings with the inverse Poletskii inequality, omitting at least one point, is equicontinuous if the majorant responsible for the distortion of the modulus of families of paths under the mapping is integrable over almost all concentric spheres centered at the given point. Since analytic functions with finite multiplicity satisfy the inverse Poletskii inequality, this result may be considered as a version of the well-known Montel theorem on the normality of families.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132869","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}

{"title":"On the number of zeros of harmonic polynomials arranged in alternating patterns","authors":"Linkui Gao,&nbsp;Gang Liu","doi":"10.1007/s13324-026-01276-6","DOIUrl":"10.1007/s13324-026-01276-6","url":null,"abstract":"<div><p>In this paper, we investigate the number of zeros of harmonic polynomials of the form </p><div><div><span>$$ f(z)=a_{1}z^{n_{1}}+a_{2}overline{z}^{n_{2}}+a_{3}z^{n_{3}}+cdots +left( frac{1+(-1)^{k+1}}{2}a_{k}z^{n_{k}}+frac{1+(-1)^{k}}{2}a_{k}overline{z}^{n_{k}}right) +a_{k+1}, $$</span></div></div><p>where <span>(a_{j}~(j=1,2cdots ,k+1))</span> are non-zero constants and <span>(n_{j}~(j=1,2cdots ,k))</span> are positive integers with <span>(n_{1}&gt;n_{2}&gt;cdots &gt;n_{k}ge 1)</span>. Assume that <i>f</i> is regular. Then we show that <i>f</i> has at least <span>(n_1+2(n_2+n_3+cdots +n_k))</span> zeros when each of its corresponding real polynomials has two distinct positive zeros. Furthermore, there are some such harmonic polynomials which have at least <span>(n_1+n_2(n_2+1))</span> zeros under particular conditions. In particular, if we choose <span>(n_1=n)</span> and <span>(n_2=n-1)</span>, then it provides an array of new examples for the sharp bound <span>(n^2)</span> of zeros of harmonic polynomials <span>(p+overline{q})</span>, where <i>p</i> and <i>q</i> are analytic polynomials with degree <i>n</i> and <span>(n-1)</span> respectively. The sharpness in case <span>(n=3)</span> is continued to be studied, and thus a sufficient condition on two parameters <i>a</i> and <i>b</i> is obtained by Cardano’s Formula for which the harmonic polynomial <span>(f(z)=z^3+aoverline{z}^2+bz+1)</span> has exactly 9 zeros.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133354","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}

{"title":"On the number of zeros of harmonic polynomials arranged in alternating patterns","authors":"Linkui Gao,&nbsp;Gang Liu","doi":"10.1007/s13324-026-01276-6","DOIUrl":"10.1007/s13324-026-01276-6","url":null,"abstract":"<div><p>In this paper, we investigate the number of zeros of harmonic polynomials of the form </p><div><div><span>$$ f(z)=a_{1}z^{n_{1}}+a_{2}overline{z}^{n_{2}}+a_{3}z^{n_{3}}+cdots +left( frac{1+(-1)^{k+1}}{2}a_{k}z^{n_{k}}+frac{1+(-1)^{k}}{2}a_{k}overline{z}^{n_{k}}right) +a_{k+1}, $$</span></div></div><p>where <span>(a_{j}~(j=1,2cdots ,k+1))</span> are non-zero constants and <span>(n_{j}~(j=1,2cdots ,k))</span> are positive integers with <span>(n_{1}&gt;n_{2}&gt;cdots &gt;n_{k}ge 1)</span>. Assume that <i>f</i> is regular. Then we show that <i>f</i> has at least <span>(n_1+2(n_2+n_3+cdots +n_k))</span> zeros when each of its corresponding real polynomials has two distinct positive zeros. Furthermore, there are some such harmonic polynomials which have at least <span>(n_1+n_2(n_2+1))</span> zeros under particular conditions. In particular, if we choose <span>(n_1=n)</span> and <span>(n_2=n-1)</span>, then it provides an array of new examples for the sharp bound <span>(n^2)</span> of zeros of harmonic polynomials <span>(p+overline{q})</span>, where <i>p</i> and <i>q</i> are analytic polynomials with degree <i>n</i> and <span>(n-1)</span> respectively. The sharpness in case <span>(n=3)</span> is continued to be studied, and thus a sufficient condition on two parameters <i>a</i> and <i>b</i> is obtained by Cardano’s Formula for which the harmonic polynomial <span>(f(z)=z^3+aoverline{z}^2+bz+1)</span> has exactly 9 zeros.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133355","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}

{"title":"Weighted Funk transforms","authors":"Rafik Aramyan","doi":"10.1007/s13324-026-01273-9","DOIUrl":"10.1007/s13324-026-01273-9","url":null,"abstract":"<div><p>We consider weighted Funk transforms on the unit 2-sphere <span>(textbf{S}^{2})</span> where the weights are given as finite Fourier series in the angle variable. We study the injectivity of the transform depending on the weight. Using the consistency method suggested by the author of this article, we obtain an injectivity condition for different classes of functions. The approach can give an inversion formula for some weights. Such inversions have theoretical significance in convexity theory, integral geometry, spherical tomography, and others.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034868","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}