Pseudodifferential operators with completely periodic symbols

Abstract

Motivated by the recent paper of Boggiatto–Garello (J Pseudo-Differ Oper Appl 11:93–117, 2020) where a Gabor operator is regarded as pseudodifferential operator with symbol $$p(x,\omega )$$ 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 $$\tau $$ τ quantization.