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Factorizations for difference operators. (English) Zbl 1347.39019

Summary: We consider the factorization problems of difference operators in \(\mathbb{C}[x;\sigma]\) for an automorphism \(\sigma\) of finite order. We study the factorization of regular polynomials in \(\mathbb{R}[x]\) in the ring of such difference operators and obtain an analogue of the fundamental theorem of algebra for skew polynomial ring \(K[x; \sigma]\) over field \(K\).

MSC:

39A70 Difference operators
47B39 Linear difference operators
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