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This is a survey paper on the subject of strong uniqueness in approximation theory. This is a survey paper on the subject of Strong Uniqueness in approximation theory. The concept of strong uniqueness was introduced by Newman, Shapiro in 1963. They proved, among other things, that if M is a finite-dimensional real Haar space in C(B), B a compact Hausdorff(More)
We establish asymptotics for Christo¤el functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain-in particular this is true if they are positive a.e on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christo¤el functions for measures(More)
×ØÖÖغ Let P d n denote the set of real algebraic polynomials of d variables and of total degree at most n. For a compact set K ⊂ Ê d set P K = sup x∈K |P (x)|. d−1 Ó. (Here, as usual, S d−1 stands for the Eucledean unit sphere in Ê d .) Furthermore, given a smooth curve Γ ⊂ Ê d , we denote by D T P the tangential derivative of P along Γ (T is the unit(More)