Abstract
In this paper, some lemmas on doubly quasi-periodic analytic functions in multiplication are proved. Such functions may not be identical to zero even if their real parts vanish on the boundary. Conditions for in which this case appears is 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lu Jian-ke, Doubly quasi-periodic Riemann boundary value problem,Acta Math. Sci.,1, 1 (1981), 13–30. (in Chinese with English abstract)
Lu Jian-ku,On the Dirichlet problems of doubly periodic analytic functions Acta Math. Sci. (English ed.),3, 4 (1983), 387–395.
Lu Jian-ku,On Dirichlet problems of doubly quasi-periodic analytic functions, Acta Math. Sci. (English ed.),5, 2 (1985)
Lu Jian-ku,Generalized theorem of residue and its applications, J. of Wuhan Univ.,3, (1978), 1–8. (in Chinese).
Author information
Authors and Affiliations
Additional information
Communicated by Chou Huan-wen
Projects supported by the Scientific Fund of the Chinese Academy of Sciences
Rights and permissions
About this article
Cite this article
Jian-ke, L. Some lemmas on doubly quasi-periodic analytic functions in multiplication. Appl Math Mech 7, 627–632 (1986). https://doi.org/10.1007/BF01895974
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01895974