Аннотация:
We investigate simultaneous Gaussian quadrature for two integrals of the same
function f but on two disjoint intervals. The quadrature nodes are zeros of a type
II multiple orthogonal polynomial for an Angelesco system. We recall some known
results for the quadrature nodes and the quadrature weights and prove some new
results about the convergence of the quadrature formulas. Furthermore we give some
estimates of the quadrature weights. Our results are based on a vector equilibrium
problem in potential theory and weighted polynomial approximation.
This is joint work with Doron Lubinsky.