Product integration of singular integrands using quasi-interpolatory splines

We consider product integrals of the form where kf L1 but f is unbounded in the integration interval. We shall approximate f by a sequence of quasi-interpolatory splines Qnf involving only function values and study the convergence of I(kQnf) to I(kf). It turns out that we can ignore an endpoint singularity but must, in general, avoid an interior singularity.