Single periodic Riemann problems for null-solutions to polynomially Cauchy–Riemann equations. Issue 6 (3rd June 2018)

• Record Type: Journal Article
• Authors: Wang, Ying; Ku, Min; Zheng, Bo
• Is Part Of: Complex variables and elliptic equations. Volume 63:Issue 6(2018)
• Page Start: 749
• Page End: 769
• Publication Date: 2018-06-03
• Subjects: Cauchy–Riemann equation -- periodic Riemann problem -- order at infinity; 30E25 -- 30G30 -- 45E05; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2017.1332597
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract: In this paper, we focus on single periodic Riemann problems for a class of meta-analytic functions, i.e. null-solutions to polynomially Cauchy–Riemann equation. We first establish decomposition theorems for single periodic meta-analytic functions. Then, we give a series expansion of single periodic meta-analytic functions, and derive generalised Liouville theorems for them. Next, we introduce a definition of order for single periodic meta-analytic functions at infinity, and characterise their growth at infinity. Finally, applying the decomposition theorem for single periodic meta-analytic functions, we get explicit expressions of solutions and condition of solvability to Riemann problems for single periodic meta-analytic functions with a finite order at infinity.