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The purpose of this paper is to show certain links between uni-variate interpolation by algebraic polynomials and the presentation of poly-harmonic functions. This allows us to construct cubature formulae for multi-variate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula… (More)

A polynomial of degree n in two variables is shown to be uniquely determined by its Radon projections taken over [n/2] + 1 parallel lines in each of the (2[(n + 1)/2] + 1) equidistant directions along the unit circle.

For any given system of continuously differentiable functions {u k } 2n k=1 which constitute an Extended Tchebycheff system of order 2 on [a, b] we prove the existence and uniqueness of the Gaussian interval quadrature formula based on n weighted integrals over non-overlapping subin-tervals of [a, b] of preassigned lengths. This supplies an analogue of the… (More)

We give a bivariate analog of the Micchelli-Rivlin quadrature for computing the integral of a function over the unit disk using its Radon projections.