Unique prime factorization in a partial semigroup of matrix-polynomials
Michael Kaltenbäck ; Harald Woracek
Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006), p. 21-43 / Harvested from The Polish Digital Mathematics Library
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We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:276846 
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Michael Kaltenbäck; Harald Woracek. Unique prime factorization in a partial semigroup of matrix-polynomials. Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006) pp. 21-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1103/

[000] [1] L. de Branges, Hilbert spaces of entire functions Prentice-Hall, London 1968. | Zbl 0157.43301

[001] [2] D. Alpay, Ya. Azizov, A. Dijksma and H. Langer, The Schur algorithm for generalized Schur functions III: J-unitary matrix polynomials on the circle, Linear Algebra Appl. 369 (2003), 113-144. | Zbl 1068.47020

[002] [3] D. Alpay, A. Dijksma and H. Langer, Factorization of J-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions, Linear Algebra Appl. 387 (2004), 313-342. | Zbl 1073.47507

[003] [4] M. Kaltenbäck and H. Woracek, Pontryagin spaces of entire functions I, Integral Equations Operator Theory 33 (1999), 34-97. | Zbl 0928.46011

[004] [5] M. Kaltenbäck and H. Woracek, Pontryagin spaces of entire functions II, Integral Equations Operator Theory 33 (1999), 305-380. | Zbl 0928.46012

[005] [6] M. Kaltenbäck and H. Woracek, Pontryagin spaces of entire functions III, Acta Sci. Math. (Szeged) 69 (2003), 241-310. | Zbl 1027.46024