András Kroó

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Let P d n be the the space of real algebraic polynomials of d variables and degree at most n, K ⊂ R a compact set, ||p||K := supx∈K |p(x)| the usual supremum norm on K, card(Y ) the cardinality of a finite set Y . A family of sets Y = {Yn ⊂ K, n ∈ N} is called an admissible mesh in K if there exists a constant c1 > 0 depending only on K such that ||p||K ≤(More)
We establish asymptotics for Christoffel 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 Christoffel functions for(More)
Let Pd n denote the set of real algebraic polynomials of d variables and of total degree at most n. For a compact set K ⊂ Rd set ‖P‖K = sup x∈K |P (x)| . Then the Markov factors on K are defined by Mn(K) := max n ‖DωP‖K : P ∈ Pd n, ‖P‖K ≤ 1 , ω ∈ Sd−1 o . (Here, as usual, Sd−1 stands for the Eucledean unit sphere in Rd .) Furthermore, given a smooth curve Γ(More)