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A Survey on the Theory of Orthogonal System and Some Open Problems

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Orthogonal Polynomials

Part of the book series: NATO ASI Series ((ASIC,volume 294))

Abstract

The present report is a brief survey of the major results established in a series of works by the author. The information we have makes it possible to conclude that these results have been overlooked by the overwhelming majority of mathematicians working in general orthogonal systems and, in particular, in orthogonal polynomials. We did not include in this report a number of the author’s results on the theory of bi-orthogonal systems, which are far-reaching generalizations of the theory of Fourier orthogonal systems in the complex domain.

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References

  1. . M. M. Djrbashian, Orthogonal systems of rational functions on the circle with given set of poles, Doklady SSSR 147(6) (1961), 1278 – 1281.

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  2. . M. M. Djrbashian, Orthogonal systems of rational functions on the circle, Izvestija AN Arm. SSR, ser. Matematika 1(1) (1966), 3–24 and 1 (2) (1966) 106 – 125.

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  3. . J. L. Walsh, Interpolation and Approximation in the Complex Domain; Amer. Math. Soc. Publ., 1950.

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  4. . G. Szegö, “Orthogonal Polynomials”, Amer. Math. Soc. Publ., 1959.

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  5. . U. Grenander and G. Szegö, “Toeplitz Forms and Their Applications”, Univ. Calif. Press, 1959.

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  6. . M. M. Djrbashian and A.A. Kitbalyan, On a generalization of the Chebyshev polynomials, Doklady AN Arm. SSR 38(5) (1964), 263 – 270.

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  7. . M. M. Djrbashian, Representation and completeness of some orthogonal systems, Izvestija AN Arm. SSR, ser. Matematika 14(6) (1979), 446 – 493.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Marshall Bagramian St. 24, B 375019, Yerevan, Armenian SSR, USSR

    M. M. Djrbashian

Authors
  1. M. M. Djrbashian
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, Ohio, USA

    Paul Nevai

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© 1990 Kluwer Academic Publishers

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Djrbashian, M.M. (1990). A Survey on the Theory of Orthogonal System and Some Open Problems. In: Nevai, P. (eds) Orthogonal Polynomials. NATO ASI Series, vol 294. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0501-6_6

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  • DOI: https://doi.org/10.1007/978-94-009-0501-6_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6711-9

  • Online ISBN: 978-94-009-0501-6

  • eBook Packages: Springer Book Archive

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