SOME LEMMAS ON DOUBLY QUASI-PERIODIC ANALYTIC FUNCTIONS IN MULTIPLICATION

<正> In this paper.some lemmas on doubly quasi-periodic analytic functions inmultiplication are proved Such functions may not be identical to zero even if their real partsvanish on the boundery. Conditions for in which this case appears is also obtained.Aconcrete example is given to show that this case actually exists. Finally,the general solutionof the considered Dirichlet problem of doubly quasi-periodic analytic functions with zeroreal parts on the boundary is obtained,provided the multipliers are not prescribed.