On the minimum of the Christoffel function

Abstract

We consider the Christoffel function λ n ( dα) associated with a measure dα 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 α with respect to the Lebesgue measure.