Riemann boundary-value problem for doubly-periodic bianalytic functions

Abstract

Abstract In this paper, we study Riemann boundary-value problem for doubly-periodic bianalytic functions. By the decomposition of doubly-periodic polyanalytic functions, the problem is transformed into two equivalent and independent Riemann boundary-value problems of doubly-periodic analytic functions, which has been discussed according to growth order of functions at the origin by Jianke Lu. Finally, we obtain the explicit expression of solutions and the conditions of solvability for the doubly-periodic bianalytic functions.

Keywords

• Doubly-periodic bianalytic function
• Riemann boundary-value problem
• Growth order
• Canonical function
• Freedom