Krein-Langer Factorization and Related Topics in the Slice Hyperholomorphic Setting

Authors

Daniel Alpay, Chapman UniversityFollow
Fabrizio Colombo, Politecnico di Milano
Irene Sabadini, Politecnico di Milano

Document Type

Article

Publication Date

2014

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 point 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.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Geometric Analysis, volume 24, issue 2, in 2014 following peer review. The final publication is available at Springer via DOI: 10.1007/s12220-012-9358-5

Recommended Citation

D. Alpay, F. Colombo and I. Sabadini. Krein-Langer factorization and related topics in the slice hyperholomorphic setting. Journal of Geometric Analysis, vol. 24 (2014), no. 2, 843-872.

Peer Reviewed

1

Copyright

Springer