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Quaternionic Wiener algebras, factorization and applications. (English) Zbl 1464.47051

The author presents an extension of certain theorems from complex analysis and operator theory to the skew field of quaternions. This consists in an almost periodic extension of the quaternionic Wiener algebra, the proof of a Wiener-Lévy-type theorem for it, factorization, and the Riemann-Hilbert problem for matrix-valued discrete and continuous algebras. The applications include solvability of two classes of quaternionic functional equations as well as rational matrix functions and canonical factorization.

MSC:

47S05 Quaternionic operator theory
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
15A66 Clifford algebras, spinors
13J05 Power series rings
15A09 Theory of matrix inversion and generalized inverses
30E25 Boundary value problems in the complex plane
30G35 Functions of hypercomplex variables and generalized variables
47B39 Linear difference operators
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References:

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