Gauss quadrature for refineable weight functions (Q1570249)

A refineable function \(\phi\) is a solution of a two-scale difference equation \[ \phi(x)= \sum_{j\in\mathbb{Z}} a_j\phi(2x- j), \] where \(a_j\) are real numbers satisfying \[ \sum_{j\in\mathbb{Z}} a_{k+ 2j}= 1,\quad\text{all }k\in\mathbb{Z}. \] The authors study Gaussian quadrature rules having refineable functions as weight functions. A discretization method is given for generating the recursion coefficients of the required orthogonal polynomials. Some numerical examples are considered.