UNIFORM RECIPROCAL APPROXIMATION SUBJECT TO COEFFICIENT CONSTRAINTS

In this paper best approximation by reciprocals of functions of a subspace U_n=span(u_1,…,u_n)satisfying coefficient constraints is considered.We present a characterization ofbest approximations.When(u_1,…,u_n)is a Descartes system an explicit characterization ofbest approximations by equioscillations is given.Existence and uniqueness results are shown.Moreover,the theory is applied to best approximaitons by reciprocals of polynomials.