Riemann-Hilbert Problems For Two Class Of Systems And Some Properties Of The Pompeiu Operator T In Quaternionic Analysis

This paper mainly studies Riemann-Hilbert boundary value problems for two class of systems. In chapter one, the Riemann-Hilbert boundary value problems for a class of nth order elliptic system is discussed. We prove its solvability and give the integral representation of the solution. In chapter two, we introduce several hyperbolic complex and generalized hyperbolic regular functions firstly, deal with the Riemann-Hilbert boundary value problems for generalized hyperbolic regular functions in the general bicylinder. We prove its solvability, give the representations of the solution and its uniqueness. In last chapter , we shown that if f ∈Lp (G),1≤p≤4,the distribution solution TG f of the inhomogeneous equation ?′z u=f on a bounded domain G in quaternionic analysis is in the space of functions Lvp (G).We also obtain the Pompeiu's formula of quaternional operator TG f.