On generalized Christoffel functions (Q1928064)

In the present paper the author studies the generalized Christoffel function \(\lambda_{p,q,n}(d\mu;x)\), \(0< p <\infty\), \(0\leq q <\infty\), with respect to a measure \(d\mu\) on \(\mathbb{R}\) defined by \[ \lambda_{p,q,n}(d\mu;x)=\min_{Q\in\mathbb P_{n-1}(x)} \int_{\mathbb{R}} \big| Q(t)\big| ^p | t-x| ^q\, d\mu(t). \] In particular, he obtains several general properties and estimates for general measures as well as for the generalized Jacobi weights.