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

摘要

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 class="mathimg" src="/content/inline/i1.gif" alt=" 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 class="mathimg" src="/content/inline/i1.gif" alt=" Riemann type problems for Hermitian monogenic and Hermitian-2-monogenic functions are solvable. Explicit representation formulas of the solutions are also given.