Sequences of orthogonal Laurent polynomials, bi-orthogonality and quadrature formulas on the unit circle

Authors:
Ruymán Cruz-Barroso;Leyla Daruis;Pablo González-Vera;Olav Njåstad
Affiliations:
Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Spain;Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Spain;Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Spain;Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper, the construction of orthogonal bases in the space of Laurent polynomials on the unit circle is considered. As an application, a connection with the so-called bi-orthogonal systems of trigonometric polynomials is established and quadrature formulas on the unit circle based on Laurent polynomials are studied.