On generalized Christoffel functions

The generalized Christoffel function lambda(p,q,n) (d mu; x) (0 <p < infinity 0 <= q < infinity) with respect to a measure d mu, on R is defined by lambda(p,q,n) (d mu; x) = inf(Q is an element of Pn-1,Q(x)=1)integral Q(t) vertical bar t - x vertical bar(q)d mu(t). The novelty of our definition is that it contains the factor vertical bar t - x vertical bar(q), which is of particular interest. Its properties are discussed and estimates are given. In particular, upper and lower bounds for generalized Christoffel functions with respect to generalized Jacobi weights are also provided.