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Quadrature Formulas on the Unit Circle and Two-Point Padé Approximation
[chapter]
1994
Nonlinear Numerical Methods and Rational Approximation II
In this paper our aim is to estimate integrals of the form [,"if} = J~... f(ei9)dl-£(8) where 1-£ is, in general a complex measure. We consider quadrature formulas like [n if} = L:7=1 Aj,nf(xj,n) with n distinct nodes Xj,n on the unit circle and so that [,"if} = [n{f} for any f E 'Rn (a certain subspace of Laurent polynomials with dimension n). Under appropriate assumptions on the function f we show that such quadratures are immediately related to the estimation of the so-called Riesz-Herglotz
doi:10.1007/978-94-011-0970-3_26
fatcat:u4mw7suuorgf7iyn2uwqatm564