Trigonometric Orthogonal Systems and Quadrature Formulae with Maximal Trigonometric Degree of Exactness
نویسندگان
چکیده
Turetzkii [Uchenye Zapiski, Vypusk 1 (149) (1959), 31–55, (English translation in East J. Approx. 11 (2005) 337–359)] considered quadrature rules of interpolatory type with simple nodes, with maximal trigonometric degree of exactness. For that purpose Turetzkii made use of orthogonal trigonometric polynomials of semi–integer degree. Ghizzeti and Ossicini [Quadrature Formulae, Academie-Verlag, Berlin, 1970], and Dryanov [Numer. Math. 67 (1994), 441–464], considered quadrature rules of interpolatory type with multiple nodes with maximal trigonometric degree of exactness. Inspired by their results, we study here s–orthogonal trigonometric polynomials of semi–integer degree. In particular, we consider the case of an even weight function.
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