Gauss-Hermite interval quadrature rule
Computers & Mathematics with Applications
Positivity and Optimization for Semi-Algebraic Functions
SIAM Journal on Optimization
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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.