The weyl calculus for group generators satisfying the canonical commutation relations

Journal article (2020)

Authors

J.M.A.M. van Neerven Analysis - EEMCS
Pierre Portal Australian National University
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2020 J.M.A.M. van Neerven, Pierre Portal
DOI: https://doi.org/10.7900/jot.2018jun13.2250
UMD spaces Canonical commutation relations H¥-functional calculus Pseudo-differential calculus Spectral multipliers Transference of C-groups Twisted convolution Weyl pairs
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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.