Theory and Application of Complex Harmonic Spline Functions

Abstract

It is well known that complex analysis has many important applications in applied sciences. But for almost all physical systems we cannot write down the explicit expressions of the solution. So we need to construct approximating functions from the given conditions. For instance, the construction of conformal mappings is an important problem both in theoretical study and in practice in various areas, (see p.53, Note 1). In this regard we would like to mention some recent developments in applications of conformal mappings: diffraction of electromagnetic waves, atomic physics, nonlinear diffusion problems, etc.. One can see its applications in various important disciplines (cf. [SL]).