Gauss-Type Quadrature Formulae for Parabolic Splines with Equidistant Knots

We construct Gauss, Lobatto, and Radau quadrature formulae associated with the spaces of parabolic splines with equidistant knots. These quadrature formulae are known to be asymptotically optimal in Sobolev spaces W p 3. Sharp estimates for the error constant in W ∞ 3 are given.