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Connection of Semi-integer Trigonometric Orthogonal Polynomials with Szegő Polynomials

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Book cover Numerical Methods and Applications (NMA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4310))

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Abstract

In this paper we investigate connection between semi-integer orthogonal polynomials and Szegő’s class of polynomials, orthogonal on the unit circle. We find a representation of the semi-integer orthogonal polynomials in terms of Szegő’s polynomials orthogonal on the unit circle for certain class of weight functions.

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

  1. Milovanović, G.V., Cvetković, A.S., Stanić, M.P.: Trigonometric quadrature formulae and orthogonal systems (submitted)

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  2. Milovanović, G.V., Djordjević, R.Ž.: Linear Algebra (in Serbian). Faculty of Electronical Engineering, Niš (2004)

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  4. 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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electronic Engineering, University of Niš, P.O. Box 73, 18000 Niš, Serbia

    Gradimir V. Milovanović, Aleksandar S. Cvetković & Zvezdan M. Marjanović

Authors
  1. Gradimir V. Milovanović
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  2. Aleksandar S. Cvetković
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  3. Zvezdan M. Marjanović
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Todor Boyanov Stefka Dimova Krassimir Georgiev Geno Nikolov

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© 2007 Springer Berlin Heidelberg

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Milovanović, G.V., Cvetković, A.S., Marjanović, Z.M. (2007). Connection of Semi-integer Trigonometric Orthogonal Polynomials with Szegő Polynomials. 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_47

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  • DOI: https://doi.org/10.1007/978-3-540-70942-8_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70940-4

  • Online ISBN: 978-3-540-70942-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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