Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line

Lixia Cao

doi:10.4236/am.2013.48165

Abstract

Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.

Highlights

Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1,2,3,4,5,6,7,8]
By using the method of complex functions, we investigate the method for solving this Riemann boundary value problem of non-normal type and give the general solutions and the solvable conditions for it
The main approach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions

Summary

Introduction

Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1,2,3,4,5,6,7,8]. By using the method of complex functions, we investigate the method for solving this Riemann boundary value problem of non-normal type and give the general solutions and the solvable conditions for it. We get the general solution in class R0 for the homogeneous problem (2) as follows For the homogeneous problem (2) in class R0 , the following two cases arise.

Objectives

Results

Conclusion