On the general solution of a functional equation on \(\mathbb{Z}\oplus\mathbb{Z}\) (Q1423781)
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scientific article; zbMATH DE number 2051596
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the general solution of a functional equation on \(\mathbb{Z}\oplus\mathbb{Z}\) |
scientific article; zbMATH DE number 2051596 |
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On the general solution of a functional equation on \(\mathbb{Z}\oplus\mathbb{Z}\) (English)
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7 March 2004
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Continuing their work in [Aequationes Math. 62, 280--285 (2001; Zbl 0992.39025) and Acta Math. Hung. 94, 93--98 (2002; Zbl 1005.39023)], the authors offer the general complex valued solution of the functional equation \(f(x+t,y+t)+f(x-t,y)+f(x,y-t)=f(x-t,y-t)+f(x,y+t)+f(x+t,y)\) on \(\mathbb Z^3\) and mention application to spatial filtering of digital images.
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functional equations
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complex valued number theoretical functions
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polynomials
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filtering
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