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Approximation of complex harmonic functions by complex harmonic splines


Authors: Han Lin Chen and Tron Hvaring
Journal: Math. Comp. 42 (1984), 151-164
MSC: Primary 30C30; Secondary 30E10, 41A15
DOI: https://doi.org/10.1090/S0025-5718-1984-0725990-8
MathSciNet review: 725990
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Abstract: In this paper, a class of complex harmonic spline functions (C.H.S.) are defined on the unit disc U. We use the C.H.S. to approximate the complex harmonic function on U, showing that C.H.S. may be represented by elementary functions. If the maximum step tends to zero and the mesh ratio is bounded, then C.H.S. converge uniformly to the interpolated function F on the closed disc Ū. If the interpolated function F is a conformal mapping, then the C.H.S. is a quasi-conformal mapping.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1984-0725990-8
Article copyright: © Copyright 1984 American Mathematical Society