Matrix Bispectrality of Full Rank One Algebras
Analysis of PDEs
2021-08-17 v1 Mathematical Physics
math.MP
Rings and Algebras
Abstract
We study algebraic properties of full rank 1 algebras in a general framework and derive a method to verify if one such matrix polynomial sub-algebra is bispectral. We give two examples illustrating the method. In the first one, we consider the eigenvalue to be scalar-valued, whereas, in the second one, we assume it to be matrix-valued. In the former example, we put forth a Pierce decomposition of that algebra.
Keywords
Cite
@article{arxiv.2108.06997,
title = {Matrix Bispectrality of Full Rank One Algebras},
author = {Brian D. Vasquez and Jorge P. Zubelli},
journal= {arXiv preprint arXiv:2108.06997},
year = {2021}
}