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On Difference Operators and their Factorization

Published online by Cambridge University Press:  20 November 2018

Patrick J. Browne  and
R. V. Nillsen
Patrick J. Browne
Affiliation:
The University of Calgary, Calgary, Alberta
R. V. Nillsen
Affiliation:
The University of Wollongong, Wollongong, New South Wales
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Throughout this paper A will be used to denote a given set and g a permutation of it. We shall assume that there is a subset C ⊆ A so that

1

Here Z denotes the set of integers. For x ∈ A it now follows that there is an unique α(x) ∈ Z so that

2

and then also

In general we shall be concerned with solving the following equation for u

3

where pi, n ≤ i ≤ r, and v are given real valued functions on A and pnpr does not vanish on A. For B ⊆ A, F(B) will denote the set of all real valued functions defined on B.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 5 , 01 October 1983 , pp. 873 - 897
Copyright
Copyright © Canadian Mathematical Society 1983

References

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