Weight functions admitting repeated positive Kronrod quadrature

In this note it is shown that for weight functions of the formw(t)=(1 –t²)^1/2/s_m(t), wheres_m is a polynomial of degreem which is positive on [–1, +1], successive Kronrod extension of a certain class ofN-point interpolation quadrature formulas, including theN-point Gauss-formula, is always possible and that each Kronrod extension has the positivity and interlacing property.