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.
Original language | English |
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Pages (from-to) | 253-298 |
Number of pages | 46 |
Journal | Journal of Operator Theory |
Volume | 83 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2020 |
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-careOtherwise 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.
Keywords
- Canonical commutation relations
- H¥-functional calculus
- Pseudo-differential calculus
- Spectral multipliers
- Transference of C-groups
- Twisted convolution
- UMD spaces
- Weyl pairs