-regular vector functions and their boundary value problems
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Boundary Value Problems 2012, 2012:75 doi:10.1186/1687-2770-2012-75Published: 19 July 2012
Let , where λ is a positive real constant. In this paper, by using the methods from quaternion calculus, we investigate the -regular vector functions, that is, the complex vector solutions of the equation , and work out a systematic theory analogous to quaternionic regular functions. Differing from that, the component functions of quaternionic regular functions are harmonic, the component functions of -regular functions satisfy the modified Helmholtz equation, that is , . We give out a distribution solution of the inhomogeneous equation and study some properties of the solution. Moreover, we discuss some boundary value problems for -regular functions and solutions of equation .
MSC: 30G35, 35J05.