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On Schur functions and Szegő orthogonal polynomials

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Topics in Interpolation Theory

Part of the book series: Operator Theory Advances and Applications ((OT,volume 95))

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Abstract

Properties of Schur functions in terms of their Schur parameters are investigated using Szegő orthogonal polynomials as a key tool. The relation between the summability of the Schur parameters and the Bernstein condition for the function to have an absolutely convergent Fourier series is discussed. It is shown that the summability of the Schur parameters implies the summability of the Taylor coefficients.

The research described in this publication was made possible in part by Grant No. U9S000 from the NSF.

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Golinskii, L. (1997). On Schur functions and Szegő orthogonal polynomials. In: Dym, H., Katsnelson, V., Fritzsche, B., Kirstein, B. (eds) Topics in Interpolation Theory. Operator Theory Advances and Applications, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8944-5_10

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  • DOI: https://doi.org/10.1007/978-3-0348-8944-5_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9838-6

  • Online ISBN: 978-3-0348-8944-5

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