Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices

Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices

We consider operators acting on a UMD Banach lattice $X$ that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\frac{1}{2}\Delta + \frac{1}{2}|x|^{2} $ acting on $L^{2}(\mathbb{R}^{d})$. More precisely, we consider abstract harmonic o...

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Bibliographic Details
Main Authors: van Neerven, Jan, Portal, Pierre, Sharma, Himani
Format: Article
Language:English
Published: Académie des sciences 2023-07-01
Series:Comptes Rendus. Mathématique
Subjects:
spectral multipliers
harmonic oscillator
twisted convolutions
canonical commutation relations
Weyl pseudo-differential calculus
UMD spaces
transference
$H^\infty $-calculus
Hörmander calculus
Online Access:https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.370/

Internet

https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.370/

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