Some lemmas on doubly quasi-periodic analytic functions in multiplication (Q1084228)

Some lemmas on doubly quasi-periodic analytic functions are proved. Such functions may not be identical to zero even if their real parts vanish on the boundary. Conditions for which this case appears are also obtained. A concrete example is given to show that this case actually exists. Finally, the general solution of the considered Dirichlet problem of doubly quasi-periodic analytic functions with zero real parts on the boundary is obtained, provided the multipliers are not prescribed.