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Uniqueness of the Gaussian extended cubature for polyharmonic functions. (English) Zbl 1111.41023
Summary: We introduce a new representation formula for the polyharmonic functions of order \(m\). We use it to prove the uniqueness of the Gaussian extended cubature for the unit ball in \(\mathbb{R}^n\) that is exact for all \(2m\)-harmonic functions and is based on surface integrals over \(m\) spheres.

MSC:
41A50 Best approximation, Chebyshev systems
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