Complex versus real orthogonal polynomials of two variables

DOI10.1080/10652469.2014.973196zbMath1312.33035arXiv1307.7819OpenAlexW2011123457MaRDI QIDQ5498534

Yuan Xu

Publication date: 9 February 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.7819

zbMATH Keywords

several variablesdisk polynomialscomplex orthogonal polynomialsorthogonal polynomials of two variablescomplex Hermite

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (6)

Multivariate holomorphic Hermite polynomials ⋮ Holomorphic Hermite polynomials in two variables ⋮ On moments of hypergeometric bivariate weight functions ⋮ Geronimus transformations of bivariate linear functionals ⋮ Generalized Characteristic Polynomials and Gaussian Cubature Rules ⋮ Classes of bivariate orthogonal polynomials

Cites Work

• Spectral properties of the Cauchy transform on \(L_2(\mathbb C,e^{-|z|^2}\lambda(z))\)
• Generalized Zernike or disc polynomials
• A class of generalized complex Hermite polynomials
• Operational formulae for the complex Hermite polynomialsH_p,q(z, z¯)
• Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle
• Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode

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