“…Almost periodic pseudo-differential operators and Gevrey classes: almost periodic pseudo-differential operators have been analyzed by numerous mathematicians including Coburn, Moyer, and Singer [206], Dedik [207], Iannacci, Bersani, Dell'Acqua, and Santucci [208], Pankov [209], Shubin [210][211][212][213], and Wahlberg [214]. In this part, we will present the main ideas and results of research study [215] by Oliaro, Rodino, and Wahlberg, only. It is well known that Shubin proved that almost periodic pseudodifferential operators act continuously on the space of smooth almost periodic functions as well as that the operator norm on L 2 equals that on the Hilbert space B 2 (R n ) of Besicovitch almost periodic functions whose Fourier coefficients are square summable.…”