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Integration of Polyharmonic Functions
Dimitar K. Dimitrov
Mathematics of Computation
Vol. 65, No. 215 (Jul., 1996), pp. 1269-1281
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2153805
Page Count: 13
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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.
Mathematics of Computation © 1996 American Mathematical Society