On the dense divergence of the product quadrature formulas of interpolatory type

This paper concerns divergent aspects regarding interpolatory product quadrature formulas generated by arbitrary projection operators associated to the Banach space C   of all real continuous functions defined on the interval [−1,1][−1,1] of RR, in supremum norm. The main result is obtained by using principles of functional analysis and it highlights the phenomenon of double condensation of singularities for the considered quadrature formulas, meaning unbounded divergence on large subsets (in topological sense) belonging to C   and to the Banach space of absolute integrable functions on [−1,1][−1,1].