Periodic decomposition of integer valued functions

Karolyi, Gy., Keletiy, T., Kos, G. and Ruzsa, I. Z. (2008) Periodic decomposition of integer valued functions. Acta Mathematica Hungarica, 119 3: 227-242. doi:10.1007/s10474-007-6217-0

Author Karolyi, Gy.
Keletiy, T.
Kos, G.
Ruzsa, I. Z.
Title Periodic decomposition of integer valued functions
Journal name Acta Mathematica Hungarica   Check publisher's open access policy
ISSN 0236-5294
Publication date 2008-05
Sub-type Article (original research)
DOI 10.1007/s10474-007-6217-0
Volume 119
Issue 3
Start page 227
End page 242
Total pages 6
Place of publication Budapest, Hungary
Publisher Akademiai Kiado
Language eng
Formatted abstract
We study those functions that can be written as a finite sum of periodic integer valued functions. On ℤ we give three different characterizations of these functions. For this we prove that the existence of a real valued periodic decomposition of a ℤ → ℤ function implies the existence of an integer valued periodic decomposition with the same periods. This result depends on the representation of the greatest common divisor of certain polynomials with integer coefficients as a linear combination of the given polynomials where the coefficients also belong to ℤ[x]. We give an example of an ℤ → {0, 1} function that has a bounded real valued periodic decomposition but does not have a bounded integer valued periodic decomposition with the same periods. It follows that the class of bounded ℤ → ℤ functions has the decomposition property as opposed to the class of bounded ℝ → ℤ functions. If the periods are pairwise commensurable or not prescribed, then we get more general results.
Keyword Periodic functions
Periodic decomposition
Integer valued and real valued functions
Difference operator
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 4 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 23 Feb 2012, 15:53:20 EST by Kay Mackie on behalf of Mathematics