Gaussian interval quadrature formulae for Tchebycheff systems

摘要

For any given system of continuously differentiable functions {u(k)}(k=1)(2n) that constitute an extended Tchebycheff system of order 2 on [a, b] we prove the existence and uniqueness of the Gaussian interval quadrature formula based on n weighted integrals over nonoverlapping subintervals of [a, b] of preassigned lengths. This supplies an analogue of the result of Krein about canonical representation of linear positive functionals.