In particular, (6) implies that the functions/i, • • • , /„ are all regular in the domain (7) a > 0, i wi\ < r, • • • ,| to„| < r. In these notations, the following theorem will be proved: Theorem. In the domain (7), let fx, • ■ • ,fnbe regular functions of the form (1) with uniformly almost periodic coefficient functions defined on (2) having Fourier expansions of the type (3), satisfying (4)....