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The Schur algorithm for generalized Schur functions III: J-unitary matrix polynomials on the circle
- Source :
- Linear Algebra and Its Applications, 369, 113-144
- Publication Year :
- 2003
- Publisher :
- Elsevier BV, 2003.
-
Abstract
- The main result is that forJ = ((1)(0) (0)(-1))every J-unitary 2 x 2-matrix polynomial on the unit circle is an essentially unique product of elementary J-unitary 2 x 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, Birkhauser Verlag, Basel, 1992; Philips J. Res. 41 (1) (1986) 1-54], and also in the first two parts [Operator Theory: Adv. Appl. 129, Birkhauser Verlag, Basel, 2000, p. 1; Monatshefte fur Mathematik, in press] of this series. The essential tool in this paper are the reproducing kernel Pontryagin spaces associated with generalized Schur functions. (C) 2003 Elsevier Science Inc. All fights reserved.
- Subjects :
- Numerical Analysis
Algebra and Number Theory
Schur's lemma
generalized Schur functions
Schur algebra
Schur polynomial
Schur's theorem
Jack function
Combinatorics
minimal factorizations
Schur decomposition
reproducing kernel Pontryagin spaces
generalized Schur algorithm
Schur complement
Discrete Mathematics and Combinatorics
kernels with negative squares
Geometry and Topology
elementary J-unitary matrix polynomials
Schur product theorem
Mathematics
Subjects
Details
- ISSN :
- 00243795
- Volume :
- 369
- Database :
- OpenAIRE
- Journal :
- Linear Algebra and its Applications
- Accession number :
- edsair.doi.dedup.....5523b4e20355f7b06a220eb2f0384ab5
- Full Text :
- https://doi.org/10.1016/s0024-3795(02)00734-6