Axisymmetric harmonic interpolation polynomials in

Author:
Morris Marden

Journal:
Trans. Amer. Math. Soc. **196** (1974), 385-402

MSC:
Primary 31B99

DOI:
https://doi.org/10.1090/S0002-9947-1974-0348130-6

MathSciNet review:
0348130

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Abstract: Corresponding to a given function which is axisymnetric harmonic in an axisymmetric region and to a set of circles in an axisymmetric subregion , an axisymmetric harmonic polynomial is found which on the interpolates to or to its partial derivatives with respect to *x*. An axisymmetric subregion is found such that converges uniformly to on the closure of *B*. Also a is determined which, together with its first *n* partial derivatives with respect to *x*, coincides with on a single circle in and converges uniformly to in a closed torus with as central circle.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0348130-6

Keywords:
Axisymmetric harmonic polynomial,
axisymmetric harmonic function,
harmonic interpolation polynomial,
Bergman operator method

Article copyright:
© Copyright 1974
American Mathematical Society