Перегляд за автором "Zhedanov, A."

Сортувати за: Порядок: Результатів:

  • A Bochner Theorem for Dunkl Polynomials 
    Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that the only families of ...
  • A ''Continuous'' Limit of the Complementary Bannai-Ito Polynomials: Chihara Polynomials 
    Genest, V.X.; Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
    A novel family of −1 orthogonal polynomials called the Chihara polynomials is characterized. The polynomials are obtained from a ''continuous'' limit of the complementary Bannai-Ito polynomials, which are the kernel partners ...
  • Bispectrality of the Complementary Bannai-Ito Polynomials 
    Genest, V.X.; Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
    A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to ...
  • Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction 
    Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, explicit expression and the weight function for ...
  • Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle 
    Tsujimoto, S.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
    Using the technique of the elliptic Frobenius determinant, we construct new elliptic solutions of the QD-algorithm. These solutions can be interpreted as elliptic solutions of the discrete-time Toda chain as well. As a ...
  • Embeddings of the Racah Algebra into the Bannai-Ito Algebra 
    Genest, V.X.; Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard realization on the space of polynomials are ...
  • From slq(2) to a Parabosonic Hopf Algebra 
    Tsujimoto, S.; Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated ...
  • Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases 
    Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
    We introduce the notion of ''hypergeometric'' polynomials with respect to Newtonian bases. We find the necessary and sufficient conditions for the polynomials Pn(x) to be orthogonal. For the special cases where the sets ...
  • Quasi-Linear Algebras and Integrability (the Heisenberg Picture) 
    Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2008)
    We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical ...