Quaternionic Wiener Algebras, Factorization and Applications
Abstract
We define an almost periodic extension of the Wiener algebras in the quaternionic setting and prove a Wiener-Levy 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.
Keywords
Cite
@article{arxiv.1605.08236,
title = {Quaternionic Wiener Algebras, Factorization and Applications},
author = {Yonatan Shelah},
journal= {arXiv preprint arXiv:1605.08236},
year = {2016}
}
Comments
34 pages, accepted for publication in AACA (Advances in Applied Clifford Algebras). The final publication will be available at Springer via http://dx.doi.org/10.1007/s00006-016-0750-2