Chebyshev-Type Integration Rules of Minimum Norm

Equal-weight integration rules are studied in the context of certain families of Hubert spaces of analytic functions defined in a family of confocal ellipses containing the interval of integration. Rules which minimize the norm of the error functional in these spaces are shown to exist and several such rules are tabulated. Asymptotic properties of these rules are studied for ellipses shrinking to the integration interval and for ellipses expanding to cover the entire plane. In the latter case, an algebraic formulation for these asymptotic rules is given and it is shown that they agree with the classical Chebyshev integration rules whenever such rules exist.