Wiener Algebra for the Quaternions

The Wiener algebra and Wiener’s lemma

Quaternions and Biquaternions: Algebra, Geometry and Physical Theories

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and ”tensor” formulation of Q-units with their possible representations are discussed and groups of Q-units transformations leaving Q-multiplication rule form-invariant are determined. A series of mathematical and physical applications is offered, among...

Some Algebraic Properties of the Wiener-laplace Algebra

— We denote by W (C+) the set of all complex-valued functions defined in the closed right half plane C+ := {s ∈ C | Re(s) ≥ 0} that differ from the Laplace transform of functions from L(0,∞) by a constant. Equipped with pointwise operations, W (C+) forms a ring. It is known that W (C+) is a pre-Bézout ring. The following properties are shown for W (C+): W (C+) is not a GCD domain, that is, ther...

Spectral factorization in the non–stationary Wiener algebra

We define the non–stationary analogue of the Wiener algebra and prove a spectral factorization theorem in this algebra.

Geometric algebra colour image representations and derived total orderings for morphological operators - Part I: Colour quaternions

Please cite this article in press as: J. Angulo, Geom I: Colour quaternions, J. Vis. Commun. (2009), d The definition of morphological operators for colour images requires a total ordering for colour points. A colour can be represented by different algebraic structures, in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied differ...