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Integration of Polyharmonic Functions

Dimitar K. Dimitrov
Mathematics of Computation
Vol. 65, No. 215 (Jul., 1996), pp. 1269-1281
Stable URL: http://www.jstor.org/stable/2153805
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Integration of Polyharmonic Functions
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Abstract

The results in this paper are motivated by two analogies. First, m-harmonic functions in Rn are extensions of the univariate algebraic polynomials of odd degree 2m - 1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.

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