Matrix Bispectrality and Noncommutative Algebras: beyond the prolate spheroidals
Functional Analysis
2022-02-02 v3 Operator Algebras
Abstract
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential operator with a simple spectrum in its commutator. In this article, we discuss a noncommutative version of the bispectral problem, obtained by allowing all objects in the original formulation to be matrix-valued. Deep attention is given to bispectral algebras and their presentations as a tool to get information about bispectral triples.
Keywords
Cite
@article{arxiv.2201.08989,
title = {Matrix Bispectrality and Noncommutative Algebras: beyond the prolate spheroidals},
author = {F. Alberto Grünbaum and Brian D. Vasquez and Jorge P. Zubelli},
journal= {arXiv preprint arXiv:2201.08989},
year = {2022}
}