Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity
Abstract
We study the link between pseudo-differential operators and Wick operators via the Bargmann transform. We deduce a formula for the symbol of the Wick operator in terms of the short-time Fourier transform of the Weyl symbol. This gives characterizations of Wick symbols of pseudo-differential operators of Shubin type and of infinite order, and results on composition. We prove a series expansion of Wick operators in anti-Wick operators which leads to a sharp G{\aa}rding inequality and transition of hypoellipticity between Wick and and Shubin symbols. Finally we show continuity results for anti-Wick operators, and estimates for the Wick symbols of anti-Wick operators.
Keywords
Cite
@article{arxiv.2011.00313,
title = {Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity},
author = {Nenad Teofanov and Joachim Toft and Patrik Wahlberg},
journal= {arXiv preprint arXiv:2011.00313},
year = {2021}
}
Comments
51 pages. This is the second version. Several new results have been added compared to the first version. Especially the part concerning hypoellipticity is new. The title is modified as well