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Open Access Research

Riemann boundary value problem for H-2-monogenic function in Hermitian Clifford analysis

Longfei Gu and Zunwei Fu*

Author Affiliations

Department of Mathematics, Linyi University, Linyi, Shandong, 276005, P.R. China

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Boundary Value Problems 2014, 2014:81  doi:10.1186/1687-2770-2014-81

Published: 9 April 2014

Abstract

Hermitian Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions of two Hermitian Dirac operators. Using a circulant matrix approach, we will study the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/81/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/81/mathml/M1">View MathML</a> Riemann type problems in Hermitian Clifford analysis. We prove a mean value formula for the Hermitian monogenic function. We obtain a Liouville-type theorem and a maximum module for the function above. Applying the Plemelj formula, integral representation formulas, and a Liouville-type theorem, we prove that the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/81/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/81/mathml/M1">View MathML</a> Riemann type problems for Hermitian monogenic and Hermitian-2-monogenic functions are solvable. Explicit representation formulas of the solutions are also given.

Keywords:
Hermitian Clifford analysis; Riemann type problems; Hermitian monogenic function