PreprintarXiv licencearXiv
An Exploration of Lacunary Orthogonal Polynomials Associated with the Geronimus Transformation
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.
Related
- A unified approach via Geronimus transformation to various types of orthogonal polynomials
- Quasi-exactly solvable deformations of quantum systems associated with exceptional orthogonal polynomials
- Matrix orthogonal polynomials related to diffference operators for L-orthogonal polynomials
- Identities and congruences involving orthogonal polynomials and Apéry-like numbers
- Time-and-band limiting for symmetric classical Dunkl orthogonal polynomials
BibTeX
@misc{bailey2026exploration,
title = {{An Exploration of Lacunary Orthogonal Polynomials Associated with the Geronimus Transformation}},
author = {Rachel Bailey and Roman Gavrilov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.06639},
eprint = {2606.06639},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.06639},
}
RIS
TY - UNPB
TI - An Exploration of Lacunary Orthogonal Polynomials Associated with the Geronimus Transformation
AU - Rachel Bailey
AU - Roman Gavrilov
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2606.06639
UR - https://arxiv.org/abs/2606.06639
AB - 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.
ER -