Lawrence A. Harris

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We obtain by elementary methods necessary and sufficient conditions for a k-dimensional cubature formula to hold for all polynomials of degree up to 2m − 1 when the nodes of the formula have Lagrange polynomials of degree at most m. The main condition is that the Lagrange polynomial at each node is a scalar multiple of the reproducing kernel of degree m − 1(More)
This note presents a Markov-type inequality for polynomials in two variables where the Chebyshev polynomials of the second kind in either one of the variables are extremal. We assume a bound on a polynomial at the set of even or odd Chebyshev nodes with the boundary nodes omitted and obtain bounds on its even or odd order directional derivatives in a(More)
This note describes a simple and efficient method of maintaining th e display for implementations of ALGOL-like languages where procedures ar e not permitted to be used as parameters. Displays were introduced by Dijkstra [2] as a means for the runtim e system of a compiler of a block-structured language to address non-loca l variables declared in blocks(More)
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