Geomathematik

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Polynomial Interpolation on the Unit Sphere and on the Unit Ball

The problem of interpolation on the unit sphere S by spherical polynomials of degree at most n is shown to be related to the interpolation on the unit ball B by polynomials of degree n. As a consequence several explicit sets of points on S are given for which the interpolation by spherical polynomials has a unique solution. We also discuss interpolation on the unit disc of R for which points are located on the circles and each circle has an even number of points. The problem is shown to be related to interpolation on the triangle in a natural way