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

2012/04/24 by Daniel Alpay, Fabrizio Colombo, Alpay, Daniel +3 · 1 citation
Mathematics · Physics and Astronomy · #30G35 #47B32 #47S10 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1204.5491

openalex publication_date 2012/04/24 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• The spectral theorem for unitary operators based on the S-spectrum

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