TY - JOUR
T1 - The weyl calculus for group generators satisfying the canonical commutation relations
AU - Van Neerven, Jan
AU - Portal, Pierre
N1 - Publisher Copyright:
© by THETA, 2020.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - 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.
AB - 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.
KW - Canonical commutation relations
KW - H¥-functional calculus
KW - Pseudo-differential calculus
KW - Spectral multipliers
KW - Transference of C-groups
KW - Twisted convolution
KW - UMD spaces
KW - Weyl pairs
UR - http://www.scopus.com/inward/record.url?scp=85088237609&partnerID=8YFLogxK
U2 - 10.7900/jot.2018jun13.2250
DO - 10.7900/jot.2018jun13.2250
M3 - Article
SN - 0379-4024
VL - 83
SP - 253
EP - 298
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 2
ER -