Quadrature Formulas on the Unit Circle and Two-point Pade Approximation

نویسندگان

  • ADHEMAR BULTHEEL
  • PABLO GONZALEZ-VERA
  • ERIK HENDRIKSEN
  • OLAV NJASTAD
چکیده

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 transform of the measure 1-£. Results concerning the rate of convergence of these quadratures are also given.

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تاریخ انتشار 2008