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Your search keyword '"reproducing kernel Pontryagin spaces"' showing total 2 results
Start Over Descriptor "reproducing kernel Pontryagin spaces" Journal linear algebra and its applications
2 results on '"reproducing kernel Pontryagin spaces"'

1. J(l)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting

Author

Heinz Langer, Daniel Alpay, and Aad Dijksma

Subjects
Numerical Analysis, Algebra and Number Theory, Generalized function, J-unitarity on the real line, elementary rational matrix functions, Unitary matrix, Rational function, Unitary state, Schur's theorem, Algebra, minimal factorizations, Factorization, reproducing kernel Pontryagin spaces, Matrix function, Schur complement, UNITARY MATRIX POLYNOMIALS, Discrete Mathematics and Combinatorics, Schur transformation, kernels with negative squares, Geometry and Topology, generalized Nevanlinna functions, Mathematics
Abstract

We introduce a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational J(l)-unitary 2 x 2 matrix functions into elementary factors from the same class. (c) 2006 Elsevier Inc. All rights reserved.

Published
2006

2. The Schur algorithm for generalized Schur functions III: J-unitary matrix polynomials on the circle

Author

Tomas Ya. Azizov, Aad Dijksma, Heinz Langer, Daniel Alpay, and Systems, Control and Applied Analysis

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
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.

Published
2003
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