Bulletin des Sciences Mathematiques最新文献

{"title":"Explicit description of Christoffel deformations and Palm measures of the Plancherel measure, the z-measures and the Gamma process","authors":"Pierre Lazag","doi":"10.1016/j.bulsci.2025.103693","DOIUrl":"10.1016/j.bulsci.2025.103693","url":null,"abstract":"<div><div>The Christoffel deformation of a measure on the real line consists of multiplying this measure by a squared polynomial having its roots in <span><math><mi>R</mi></math></span>. We introduce Christoffel deformations of discrete orthogonal polynomial ensembles by considering the Christoffel deformations of the underlying measure, and prove that this construction extends to more general point processes describing distributions on partitions: the poissonized Plancherel measure and the <em>z</em>-measures. These deformations contain the theory of Palm measures, and as a consequence, we obtain explicit formulas for the Palm measures of the poissonized Plancherel measure and the <em>z</em>-measures in terms of discrete Wronskians in the relevant special functions. The extension to the Plancherel measure is obtained via a limit transition from the Charlier ensemble, while the extension to the <em>z</em>-measures follows from an analytic continuation argument. A limit procedure starting from the non-degenerate <em>z</em>-measures leads to a deformation of the Gamma process introduced by Borodin and Olshanski.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103693"},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513642","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":"Invariants of group representations, dimension/degree duality and normal forms of vector fields","authors":"Ewa Stróżyna ,&nbsp;Henryk Żoła̧dek","doi":"10.1016/j.bulsci.2025.103685","DOIUrl":"10.1016/j.bulsci.2025.103685","url":null,"abstract":"<div><div>We develop an analytic approach to the problem of polynomial first integrals for linear vector fields. As an application we obtain a new proof of the theorem of Maurer and Wietzenböck about finiteness of the number of generators of the ring of constants of a linear derivation in the polynomial ring.</div><div>In the case of linear nilpotent vector field <strong><em>X</em></strong> with one Jordan cell we deal with an irreducible representation Sym<span><math><mmultiscripts><mrow><mi>V</mi></mrow><mprescripts></mprescripts><none></none><mrow><mi>n</mi></mrow></mmultiscripts></math></span>, <span><math><mi>V</mi><mo>=</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, of the Lie algebra <span><math><mrow><mi>sl</mi></mrow><mo>(</mo><mn>2</mn><mo>)</mo></math></span>. The homogeneous polynomial first integrals of <strong><em>X</em></strong> of degree <em>d</em> correspond to highest weight vectors in the representation Sym<span><math><mmultiscripts><mrow><mo>(</mo><msup><mrow><mi>Sym</mi></mrow><mrow><mi>n</mi></mrow></msup><mi>V</mi><mo>)</mo></mrow><mprescripts></mprescripts><none></none><mrow><mi>d</mi></mrow></mmultiscripts></math></span>. We present a generating function for the multiplicities of the splitting of the latter representation into irreducible ones.</div><div>The dim/deg duality is an isomorphism Sym<span><math><mmultiscripts><mrow><mo>(</mo><msup><mrow><mi>Sym</mi></mrow><mrow><mi>n</mi></mrow></msup><mi>V</mi><mo>)</mo></mrow><mprescripts></mprescripts><none></none><mrow><mi>d</mi></mrow></mmultiscripts><mo>≃</mo></math></span> Sym<span><math><mmultiscripts><mrow><mo>(</mo><msup><mrow><mi>Sym</mi></mrow><mrow><mi>d</mi></mrow></msup><mi>V</mi><mo>)</mo></mrow><mprescripts></mprescripts><none></none><mrow><mi>n</mi></mrow></mmultiscripts></math></span>. We give a functional analytic construction of the duality map.</div><div>Using a transvectant formula we obtain a new relation for the elementary symmetric polynomials.</div><div>Finally, we propose an alternative approach to the analyticity property of the normal form reduction of a germ of vector field with nilpotent linear part in a case considered by Stolovich and Verstringe.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103685"},"PeriodicalIF":1.3,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338704","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":"A new formal series method and its application to the center problem in Z2-equivariant nilpotent vector fields","authors":"Feng Li ,&nbsp;Yusen Wu ,&nbsp;Ting Chen ,&nbsp;Pei Yu","doi":"10.1016/j.bulsci.2025.103684","DOIUrl":"10.1016/j.bulsci.2025.103684","url":null,"abstract":"<div><div>In this paper, center problems and bifurcation of limit cycles are considered for <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-equivariant nilpotent vector fields. A new formal series method is developed for computing the focal values of the vector fields, which can be conveniently implemented using a computer algebraic system. As an application, the new method is applied to classify the centers for a class of quintic-order systems, which contains four conditions associated with a nilpotent singular point at the origin and two center conditions associated with an elementary center at infinity. Moreover, eight small-amplitude limit cycles in the neighborhood of the origin and nine large-amplitude limit cycles at infinity are obtained. This is the first time to investigate the synchronous bifurcation problem associated with a nilpotent singular point at the origin and a Hopf singular point at infinity.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103684"},"PeriodicalIF":1.3,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322168","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":"Convergence of sub-series' and sub-signed series' in terms of the asymptotic ψ-density","authors":"Janne Heittokangas ,&nbsp;Zinelaabidine Latreuch","doi":"10.1016/j.bulsci.2025.103683","DOIUrl":"10.1016/j.bulsci.2025.103683","url":null,"abstract":"<div><div>Given a non-negative real sequence <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>n</mi></mrow></msub></math></span> such that the series <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> diverges, it is known that the size of an infinite subset <span><math><mi>A</mi><mo>⊂</mo><mi>N</mi></math></span> can be measured in terms of the linear density such that the sub-series <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>∈</mo><mi>A</mi></mrow></msub><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> either (a) converges or (b) still diverges. The purpose of this research is to study these convergence/divergence questions by measuring the size of the set <span><math><mi>A</mi><mo>⊂</mo><mi>N</mi></math></span> in a more precise way in terms of the recently introduced asymptotic <em>ψ</em>-density. The convergence of the associated sub-signed series <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is also discussed, where <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>n</mi></mrow></msub></math></span> is a real sequence with values restricted to the set <span><math><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103683"},"PeriodicalIF":1.3,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144312917","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":"Approximation of Schrödinger operators with point interactions on bounded domains","authors":"Diego Noja ,&nbsp;Raffaele Scandone","doi":"10.1016/j.bulsci.2025.103671","DOIUrl":"10.1016/j.bulsci.2025.103671","url":null,"abstract":"<div><div>We consider Schrödinger operators on a bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, with homogeneous Robin or Dirichlet boundary conditions on ∂Ω and a point (zero-range) interaction placed at an interior point of Ω. We show that, under suitable spectral assumptions, and by means of an extension-restriction procedure which exploits the already known result on the entire space, the singular interaction is approximated by rescaled sequences of regular potentials. The result is missing in the literature, and we also take the opportunity to point out some general issues in the approximation of point interactions and the role of zero energy resonances.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103671"},"PeriodicalIF":1.3,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239635","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":"Hausdorff measure of zeros of nontrivial multivariable polynomials","authors":"Andrew Murdza,&nbsp;Khai T. Nguyen,&nbsp;Etienne Phillips","doi":"10.1016/j.bulsci.2025.103681","DOIUrl":"10.1016/j.bulsci.2025.103681","url":null,"abstract":"<div><div>This paper establishes a sharp universal bound on the <span><math><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-dimensional Hausdorff measure of the zero level set of any nontrivial multivariable polynomial <span><math><mi>p</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>→</mo><mi>R</mi></math></span> within <em>d</em>-dimensional cubes of size <em>r</em>. The bound depends only on the cube size <em>r</em>, the dimension <em>d</em>, and the degrees of the polynomial <em>p</em>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103681"},"PeriodicalIF":1.3,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270238","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":"Reproducing formulas for operator-valued Gabor frames on LCA groups","authors":"Jingsheng Wang,&nbsp;Pengtong Li","doi":"10.1016/j.bulsci.2025.103682","DOIUrl":"10.1016/j.bulsci.2025.103682","url":null,"abstract":"<div><div>In this article, we investigate the reproducing formulas of operator-valued Gabor frames on an LCA group <em>G</em> with time-frequency shifts along a closed subgroup of the phase space. We first determine conditions on generators of such operator-valued systems that provide reproducing formulas of functions in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. Then the weak density theorem, the Janssen representation and the Bessel duality principle for operator-valued Gabor systems are obtained. These extend well-established results on classical Gabor systems. While our partial results are similar to one of Gabor g-frames on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, introduced by E. Skrettingland <span><span>[29]</span></span>, our methods are completely different, which provide new ideas of studying OPV-Gabor frames.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103682"},"PeriodicalIF":1.3,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262610","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":"Measure attractors of stochastic Schrödinger lattice systems driven by nonlinear noise","authors":"Shaoyue Mi ,&nbsp;Ran Li ,&nbsp;Dingshi Li","doi":"10.1016/j.bulsci.2025.103672","DOIUrl":"10.1016/j.bulsci.2025.103672","url":null,"abstract":"<div><div>This paper focuses on the measure attractors of stochastic Schrödinger equations driven by infinite-dimensional nonlinear noise on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. We begin by introducing the fundamental concepts of measure attractors and the asymptotic compactness of such systems. Subsequently, we establish a general theorem concerning the existence, uniqueness, and structural properties of measure attractors. Finally, we apply this abstract framework to analyze the measure attractors of stochastic Schrödinger lattice systems.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103672"},"PeriodicalIF":1.3,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239634","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":"The spectral analysis of the difference quotient operator on model spaces","authors":"Carlo Bellavita ,&nbsp;Eugenio Dellepiane ,&nbsp;Javad Mashreghi","doi":"10.1016/j.bulsci.2025.103673","DOIUrl":"10.1016/j.bulsci.2025.103673","url":null,"abstract":"<div><div>We conduct a spectral analysis of the difference quotient operator <span><math><msubsup><mrow><mtext>Q</mtext></mrow><mrow><mi>ζ</mi></mrow><mrow><mi>u</mi></mrow></msubsup></math></span>, associated with a boundary point <span><math><mi>ζ</mi><mo>∈</mo><mo>∂</mo><mi>D</mi></math></span>, on the model space <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span>. We describe the operator's spectrum and provide both upper and lower estimates for its norm <span><math><mo>‖</mo><msubsup><mrow><mtext>Q</mtext></mrow><mrow><mi>ζ</mi></mrow><mrow><mi>u</mi></mrow></msubsup><mo>‖</mo></math></span>, and furthermore discussing the sharpness of these bounds. Notably, the upper estimate offers a new characterization of the one-component property for inner functions.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103673"},"PeriodicalIF":1.3,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204789","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":"Minimal presentation, finite quotients and lower central series of cactus groups","authors":"Hugo Chemin,&nbsp;Neha Nanda","doi":"10.1016/j.bulsci.2025.103669","DOIUrl":"10.1016/j.bulsci.2025.103669","url":null,"abstract":"<div><div>This article deals with the study of cactus groups from a combinatorial point of view. These groups have been gaining prominence lately in various domains of mathematics, amongst which are their relations with well-known groups such as braid groups, diagram groups, to name a few. We compute a minimal presentation for cactus groups in terms of generators and non-redundant relations. We also construct homomorphisms of these groups onto certain finite groups, which leads to results about finite quotients of cactus groups. More precisely, we construct homomorphisms onto the universal Coxeter group and prove that all (infinite) dihedral groups appear as quotients of cactus groups. This further facilitate the investigation of the lower central series and its consecutive quotients. While there are already known established similarities with braid groups, we deduce a considerable disparity between the two groups.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103669"},"PeriodicalIF":1.3,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221695","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}