Pseudodifferential operators with completely periodic symbols

Abstract

Motivated by the recent paper of Boggiatto-Garello in J. Pseudo-Differ. Oper. Appl. 11 (2020), 93-117, where a Gabor operator is regarded as pseudodifferential operator with symbol $p(x,ω)$ periodic on both the variables, we study the continuity and invertibility, on general time frequency invariant spaces, of pseudodifferential operators with completely periodic symbol and general $τ$ quantization.