Abstract
In this paper, we present and study a kind of Riemann boundary value problem of non-normal type for analytic functions on two parallel curves. Making use of the method of complex functions, we give the method for solving this kind of doubly periodic Riemann boundary value problem of non-normal type and obtain the explicit expressions of solutions and the solvable conditions for it.
Highlights
Classical Riemann boundary value problems (RBVPs), doubly periodic or quasi-periodic RBVPs and Dirichlet Problems for analytic functions or for polyanalytic functions, on closed curves or on open arcs, have been widely investigated in papers [1]-[8]
The main approach is to use the decomposition of polyanalytic functions and their generalization to transform the given boundary value problems to their corresponding boundary value problems for analytic functions, and the fundamental and important tool for which is the Plemelj formula
Xing proposed the Periodic Riemann Boundary Value Inverse Problems in paper [9], and various inverse RBVPs for generalized analytic functions or bianalytic functions have been investigated in papers [10]-[13]
Summary
Classical Riemann boundary value problems (RBVPs), doubly periodic or quasi-periodic RBVPs and Dirichlet Problems for analytic functions or for polyanalytic functions, on closed curves or on open arcs, have been widely investigated in papers [1]-[8]. Xing proposed the Periodic Riemann Boundary Value Inverse Problems in paper [9], and various inverse RBVPs for generalized analytic functions or bianalytic functions have been investigated in papers [10]-[13]. We present a kind of doubly periodic RBVP of non-normal type for analytic functions on two parallel curves. (2015) Doubly Periodic Riemann Boundary Value Problem of Non-Normal Type for Analytic Functions on Two Parallel Curves.
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