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TRIGONOMETRIC MULTIPLE ORTHOGONAL POLYNOMIALS OF SEMI-INTEGER DEGREE AND
THE CORRESPONDING QUADRATURE FORMULAS
Gradimir V. Milovanovic, Marija P. Stanic, and Tatjana V. Tomovic
Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia and Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Abstract: An optimal set of quadrature formulas with an odd number of nodes for trigonometric polynomials in Borges' sense [Numer. Math. 67 (1994), 271–288], as well as trigonometric multiple orthogonal polynomials of semi-integer degree are defined and studied. The main properties of such a kind of orthogonality are proved. Also, an optimal set of quadrature rules is characterized by trigonometric multiple orthogonal polynomials of semi-integer degree. Finally, theoretical results are illustrated by some numerical examples.
Classification (MSC2000): 42C05; 65D32
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