Ge´za Freud, orthogonal polynomials and Christoffel functions. A case study
Journal of Approximation Theory
Generalized Gaussian quadrature formulas
Journal of Approximation Theory
On Christoffel type functions for Lm extremal polynomials
Journal of Approximation Theory
Christoffel type functions for m-orthogonal polynomials
Journal of Approximation Theory
Full length articles: On the zeros of m-orthogonal polynomials for Freud weights
Journal of Approximation Theory
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This paper gives upper and lower bounds of the Christoffel-type functions @l"j"n(W^m,m;x),j=m-2,m-4,...,m-2[m/2], for the m-orthogonal polynomials for a Freud weight W=e^-^Q, which are given as follows. Let a"n=a"n(Q) be the nth Mhaskar-Rahmanov-Saff number, @f"n(x)=max{n^-^2^/^3,1-|x|/a"n}, and d0. Assume that Q@?C(R) is even, Q^''@?C[0,~),Q^'(x)0,x@?(0,~),Q(0)=0, and for some A,B1A==ca"nn^j^+^1W(x)^m@f"n(x)^-^1^/^2,miseven,j=0,ca"nn^j^+^1W(x)^motherwise,and for |x|=