Commutators on Fock spaces
Mathematical Physics
2023-04-19 v1 math.MP
Abstract
Given a weighted space with weights associated to an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond-Leontiev derivatives. This general class of operators includes many known examples, like classic fractional derivatives and Dunkl operators. This allows us to establish a general framework which goes beyond the classic Weyl-Heisenberg algebra. Concrete examples for its application are provided.
Cite
@article{arxiv.2208.03394,
title = {Commutators on Fock spaces},
author = {Daniel Alpay and Paula Cerejeiras and Uwe Kaehler and Trevor Kling},
journal= {arXiv preprint arXiv:2208.03394},
year = {2023}
}