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Quaternionic Wiener Algebras, Factorization and Applications

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Abstract

We define an almost periodic extension of the Wiener algebras in the quaternionic setting and prove a Wiener–Lévy type theorem for it, as well as extending the theorem to the matrix-valued case. We prove a Wiener–Hopf factorization theorem for the quaternionic matrix-valued Wiener algebras (discrete and continuous) and explore the connection to the Riemann–Hilbert problem in that setting. As applications, we characterize solvability of two classes of quaternionic functional equations and give an explicit formula for the canonical factorization of quaternionic rational matrix functions via realization.

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Authors and Affiliations

  1. Department of Mathematics, Tel Aviv University, University of Michigan and School of Mathematics, Ann Arbor, Michigan, USA

    Yonatan Shelah

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  1. Yonatan Shelah
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Correspondence to Yonatan Shelah.

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Communicated by Rafał Abłamowicz

This paper is based on the author’s MSc thesis, which was written when he was a student at Tel Aviv University. The author would like to thank his advisor, Prof. Daniel Alpay, for introducing him to quaternionic analysis and proposing which topics to tackle. His input and encouragement were most valuable.

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Shelah, Y. Quaternionic Wiener Algebras, Factorization and Applications. Adv. Appl. Clifford Algebras 27, 2805–2840 (2017). https://doi.org/10.1007/s00006-016-0750-2

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  • DOI: https://doi.org/10.1007/s00006-016-0750-2

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