Chebyshev Approximation Using a Generalized Weight Function

is a best approximation to f. The base functions are assumed to be linearly independent, so that P(x; a) = 0 for all x E X implies a = (0, 0, * , 0). To define best approximation, let W(x, y) be a function defined for x C X, y C (-oc, c ) with values in the extended reals [-oo, oo ] and properties to be given later. The function W(x, y) is called a generalized weight function. A polynomial P(x; a) is said to approximate f if