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The weyl calculus for group generators satisfying the canonical commutation relations

Journal Article (2020)
Author(s)

Jan Van Neerven (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Pierre Portal (The Australian National University)

Research Group
Analysis
DOI related publication
https://doi.org/10.7900/jot.2018jun13.2250 Final published version
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Publication Year
2020
Language
English
Research Group
Analysis
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Journal title
Journal of Operator Theory
Issue number
2
Volume number
83
Pages (from-to)
253-298
Downloads counter
253
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Institutional Repository
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Abstract

We generalise the classical Weyl pseudo-differential calculus on Rd to the setting of two d-tuples of operators A = (A1,..., Ad) and B = (B1,..., Bd) acting on a Banach space generating bounded C0-groups satisfying the Weyl canonical commutation relations. We show that the resulting Weyl calculus extends to symbols in the standard symbol class S0 provided appropriate bounds can be established. Using transference techniques we obtain boundedness of the H∞-functional calculus (and even the Hormander calculus), for the abstract harmonic oscillator.

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