Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions
Sign Up to like & getrecommendations! Published in 2017 at "Reports on Mathematical Physics"
DOI: 10.1016/s0034-4877(18)30040-5
Abstract: We propose a set of polynomials orthonormal under a general weight which are symmetrical tensors in D -dimensional Euclidean space. The D -dimensional Hermite polynomials are shown to be a particular case of the present… read more here.
Keywords: orthonormal polynomials; chebyshev legendre; physics; polynomials dimensions ... See more keywords
Conformal equivalence of measures and dynamics of orthogonal polynomials
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2019.1648446
Abstract: ABSTRACT We introduce a notion of asymptotically orthonormal polynomials for a Borel measure μ with compact non-polar support in . Such sequences of polynomials have similar convergence properties of the sequences of Julia sets and… read more here.
Keywords: asymptotically orthonormal; dynamics orthogonal; orthonormal polynomials; convergence properties ... See more keywords
Zernike-like Laguerre-Gaussian orthonormal polynomials for optical field reconstruction.
Sign Up to like & getrecommendations! Published in 2022 at "Optics letters"
DOI: 10.1364/ol.475979
Abstract: Analytic closed form expressions for orthonormal polynomials exhibiting both rotational and Gaussian symmetries are derived for both circular and elliptical geometries. They exhibit a close correspondence to the Zernike polynomials but are of Gaussian shape… read more here.
Keywords: orthonormal polynomials; like laguerre; reconstruction; zernike like ... See more keywords