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arXiv · 1204.5491

Krein-Langer factorization and related topics in the slice hyperholomorphic setting

Daniel Alpay·Fabrizio Colombo·Irene Sabadini
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Abstract

We study various aspects of Schur analysis in the slice hyperholomorphic setting. We present two sets of results: first, we give new results on the functional calculus for slice hyperholomorphic functions. In particular, we introduce and study some properties of the Riesz projectors. Then we prove a Beurling-Lax type theorem, the so-called structure theorem. A crucial fact which allows to prove our results, is the fact that the right spectrum of a quaternionic linear operator and the S-spectrum coincide. Finally, we study the Krein-Langer factorization for slice hyperholomorphic generalized Schur functions. Both the Beurling-Lax type theorem and the Krein-Langer factorization are far reaching results which have not been proved in the quaternionic setting using notions of hyperholomorphy other than slice hyperholomorphy

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Daniel Alpay, Fabrizio Colombo, Irene Sabadini. 2012-11-13. Krein-Langer factorization and related topics in the slice hyperholomorphic setting. https://arxiv.org/abs/1204.5491

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