An Exploration of Lacunary Orthogonal Polynomials Associated with the Geronimus Transformation
Year: 2026
Type: preprint
Abstract: In this note, we present two perturbations of sequences of orthogonal polynomials related to two iterations of the Geronimus transformation, with the feature that the resulting sequences of polynomials are missing a single degree. We relate these sequences to quasi-orthogonal polynomials of order 2 and investigate properties including recurrence relations, completeness, and associated differential equations.
Source: arXiv (Cornell University)
Authors: Bailey, Rachel, Gavrilov, Roman
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163923780