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arXiv · 2208.03394

Commutators on Fock spaces

Daniel Alpay·Paula Cerejeiras·Uwe Kaehler·Trevor Kling
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Abstract

Given a weighted $\ell^2$ 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.

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Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Trevor Kling. 2022-08-05. Commutators on Fock spaces. https://doi.org/10.1063/5.0080723

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