On the minimum of the Christoffel function

[摘要] We consider the Christoffel function lambda(n)(d alpha) associated with a measure d alpha on a compact interval and the question where the minimum of the Christoffel function is attained. Sufficient conditions on the coefficients appearing in the continued fraction expansion of the Stieltjes transform are obtained for the nth Christoffel function to attain its minimum at the boundary points of the underlying interval. In contrary to several monotonicity results for Christoffel functions in the literature, our approach does not require the absolute continuity of the measure alpha with respect to the Lebesgue measure.

[发布日期] 1995-12-29

[效力级别]  Proceedings Paper

[关键词] Christoffel function;weighted approximation;orthogonal polynomials;continued fractions;Stieltjes transform