Title

The Schur Algorithm for Generalized Schur Functions III: Reproducing Kernels

Document Type

Article

Publication Date

2003

Abstract

The main result is that for
J=100−1
every J-unitary 2×2-matrix polynomial on the unit circle is an essentially unique product of elementary J-unitary 2×2-matrix polynomials which are either of degree 1 or 2k. This is shown by means of the generalized Schur transformation introduced in [Ann. Inst. Fourier 8 (1958) 211; Ann. Acad. Sci. Fenn. Ser. A I 250 (9) (1958) 1–7] and studied in [Pisot and Salem Numbers, Birkhäuser Verlag, Basel, 1992; Philips J. Res. 41 (1) (1986) 1–54], and also in the first two parts [Operator Theory: Adv. Appl. 129, Birkhäuser Verlag, Basel, 2000, p. 1; Monatshefte für Mathematik, in press] of this series. The essential tool in this paper are the reproducing kernel Pontryagin spaces associated with generalized Schur functions.

Comments

This article was originally published in Linear Algebra and its Applications, volume 369, in 2003. DOI: 10.1016/S0024-3795(02)00734-6

Peer Reviewed

1

Copyright

Elsevier