Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity

Autor:	Teofanov, Nenad, Toft, Joachim, Wahlberg, Patrik
Rok vydání:	2020
Předmět:	Mathematics - Functional Analysis Mathematics - Complex Variables Mathematics - Operator Algebras Primary: 32W25 35S05 32A17 46F05 42B35 Secondary: 32A25 32A05
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.00313 Zobrazit plný text záznamu View this record from Arxiv