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A Generalized Pell's equation for a class of multivariate orthogonal polynomials

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  • معلومة اضافية
    • Contributors:
      Equipe Polynomial OPtimization (LAAS-POP); Laboratoire d'analyse et d'architecture des systèmes (LAAS); Université Toulouse Capitole (UT Capitole); Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse); Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J); Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3); Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP); Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole); Université de Toulouse (UT); Toulouse School of Economics (TSE-R); Université de Toulouse (UT)-Université de Toulouse (UT)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE); Department of Mathematics, University of Oregon Eugene; University of Oregon Eugene; ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019)
    • بيانات النشر:
      CCSD
      American Mathematical Society
    • الموضوع:
      2024
    • نبذة مختصرة :
      To appear in Transactions of the Amercian Mathematical Society ; International audience ; We extend the polynomial Pell's equation satisfied by univariate Chebyshev polynomials on [−1, 1] from one variable to several variables, using orthogonal polynomials on regular domains that include cubes, balls, and simplexes of arbitrary dimension. Moreover, we show that such an equation is strongly connected (i) to a certificate of positivity (from real algebraic geometry) on the domain, as well as (ii) to the Christoffel functions of the equilibrium measure on the domain. In addition, the solution to Pell's equation reflects an extremal property of orthonormal polynomials associated with an entropy-like criterion.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2307.10668; ARXIV: 2307.10668
    • الرقم المعرف:
      10.1090/tran/9200
    • الدخول الالكتروني :
      https://laas.hal.science/hal-04163153
      https://laas.hal.science/hal-04163153v2/document
      https://laas.hal.science/hal-04163153v2/file/BX-revised.pdf
      https://doi.org/10.1090/tran/9200
    • Rights:
      http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.732F077