Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials

Authors:
E. Berriochoa;A. Cachafeiro;J. García Amor
Affiliations:
Departamento de Matemática Aplicada I, Facultad de Ciencias Ourense, Universidad de Vigo, 32004 Ourense, Spain;Departamento de Matemática Aplicada I, E.T.S. Ingenieros Industriales, Universidad de Vigo, 36310 Vigo, Spain;Departamento de Matemática Aplicada I, E.T.S. Ingenieros Industriales, Universidad de Vigo, 36310 Vigo, Spain
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 3
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Abstract

In the present paper we characterize the measures on the unit circle for which there exists a quadrature formula with a fixed number of nodes and weights and such that it exactly integrates all the polynomials with complex coefficients. As an application we obtain quadrature rules for polynomial modifications of the Bernstein measures on [-1,1], having a fixed number of nodes and quadrature coefficients and such that they exactly integrate all the polynomials with real coefficients.