Year: 2016
Type: article
Abstract: A classical result due to Bochner classifies the orthogonal polynomials on the real line which are common eigenfunctions of a second order linear differential operator.We settle a natural version of the Bochner problem on the unit circle which answers a similar question concerning orthogonal Laurent polynomials and can be formulated as a bispectral problem involving CMV matrices.We solve this CMV bispectral problem in great generality proving that, except the Lebesgue measure, no other one on the unit circle yields a sequence of orthogonal Laurent polynomials which are eigenfunctions of a linear differential operator of arbitrary order.Actually, we prove that this is the case even if such an eigenfunction condition is imposed up to finitely many orthogonal Laurent polynomials.three workers at Bell Labs in the 1960s: David Slepian, Henry Landau, and Henry Pollak, see [32,33,[42][43][44][45][46].The most important of these miracles is the existence of a second order
DOI: 10.1093/imrn/rnw186
Authors: Francisco Alberto Grünbaum, Luis Velázquez
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2467967301