Abstract
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.
The authors were supported in part by the Serbian Ministry of Science and Environmental Protection (Project: Orthogonal Systems and Applications, grant number #144004) and the Swiss National Science Foundation (SCOPES Joint Research Project No. IB7320–111079 “New Methods for Quadrature”).
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References
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Milovanović, G.V., Cvetković, A.S., Stanić, M.P.: Trigonometric quadrature formulae and orthogonal systems (submitted)
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Turetzkii, A.H.: On quadrature formulae that are exact for trigonometric polynomials (English translation from Uchenye Zapiski, Vypusk 1 (149), Seria math. Theory of Functions, Collection of papers, Izdatel’stvo Belgosuniversiteta imeni V.I. Lenina, Minsk (1959) 31–54). East J. Approx. 11, 337–359 (2005)
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Milovanović, G.V., Cvetković, A.S., Stanić, M.P. (2007). Trigonometric Orthogonal Systems and Quadrature Formulae with Maximal Trigonometric Degree of Exactness. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_48
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DOI: https://doi.org/10.1007/978-3-540-70942-8_48
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