Chebyshev-Type Quadratures for Doubling Weights

A Chebyshev-type quadrature for a given weight function is a quadrature formula with equal weights. In this work, we show that a method presented by Kane may be used to determine the order of magnitude of the minimal number of nodes required in Chebyshev-type quadratures for doubling weight functions. This extends a long line of research on Chebyshev-type quadratures starting with the 1937 work of Bernstein.