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Dynamical Systems of Operators Induced by Scaled Hypercomplex Rings

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Abstract

In this paper, we consider a family of the hypercomplex rings \({\mathscr {H}}=\left\{ {\mathbb {H}}_{t}\right\} _{t\in {\mathbb {R}}}\) scaled by \({\mathbb {R}}\), and the dynamical system of \({\mathbb {R}}\) acting on \({\mathscr {H}}\) via a certain action \(\theta \) of \({\mathbb {R}}\). i.e., we study an analysis on dynamical system induced by \({\mathscr {H}}\). In particular, we are interested in free-probabilistic information on the dynamical system dictated by our hypercomplex analysis.

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Authors and Affiliations

  1. Department of Mathematics, Chapman University, 1 University Dr., Orange, CA, 92866 1288, USA

    Daniel Alpay

  2. St. Ambrose Univ., Dept. of Math. & Stat., 518 W. Locust, St. Davenport, lowa, 52803, USA

    Ilwoo Cho

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  1. Daniel Alpay
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  2. Ilwoo Cho
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Correspondence to Daniel Alpay.

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Communicated by Uwe Kaehler.

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Alpay, D., Cho, I. Dynamical Systems of Operators Induced by Scaled Hypercomplex Rings. Adv. Appl. Clifford Algebras 33, 33 (2023). https://doi.org/10.1007/s00006-023-01272-0

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