arXiv 2201.089892022-01math.FAmath.OA

Matrix Bispectrality and Noncommutative Algebras: beyond the prolate spheroidals

F. Alberto Grünbaum, Brian D. Vasquez, Jorge P. Zubelli

英文摘要：

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.

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