Moebius transforms

  • Adhemar Bultheel
Part of the Operator Theory: Advances and Applications book series (OT, volume 27)


In this chapter we shall again look in more detail at the recurrence (3.6). Chapter 5 exhausted the interpretation of (3.6) in terms of CFs. Now we shall interpret (3.6) as a sequence of Moebius transforms for series. In this way we shall obtain an nonhomogeneous version of algorithm 2 and of an inverse for algorithm 1. In the special case that F(z) for z = exp(iθ) represents the Fourier expansion of a positive function, the reformulation of algorithm 2 will turn out to be the algorithm as originally formulated by Schur. The inverse of algorithm 1 as we shall formulate it, becomes the classical Schur-Cohn test to check if the zeros of a polynomial are inside the unit disc. These facts will be explained in chapter 17.


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Copyright information

© Birkhäuser Verlag Basel 1987

Authors and Affiliations

  • Adhemar Bultheel
    • 1
  1. 1.Dept. Computer ScienceK. U. LeuvenLeuven-HeverleeBelgium

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