1. On the theorem of M Golomb.
- Author
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Ismailov, Vugar E.
- Subjects
- *
APPROXIMATION theory , *DUALITY theory (Mathematics) , *BOLTS & nuts , *ORTHOGONAL polynomials , *MATHEMATICS - Abstract
Let X1, … , Xn be compact spaces and X = X1 x…xXn. Consider the approximation of a function f ϵ C(X) by sums g1(x1)+…+gn(xn), where gi ϵ C(Xi ), i = 1, … , n. In [8], Golomb obtained a formula for the error of this approximation in terms of measures constructed on special points of X, called 'projection cycles'. However, his proof had a gap, which was pointed out by Marshall and O'Farrell [15]. But the question if the formula was correct, remained open. The purpose of the paper is to prove that Golomb's formula holds in a stronger form. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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