Summary.
Without assuming regularity we answer the questions when from a connected open set \(D \subset {\mathbb{R}}^2\) there exist quasiextensions of the Cauchy equation
$$e(s + t) = e(s)e(t)\quad ((s, t) \in D)$$
and extensions of the Pexider equation
$$f(s + t) = g(s)h(t)\quad ((s, t) \in D)$$
to \({\mathbb{R}}^2\). Even when no (quasi) extensions exist, we determine the general solutions (both with and without regularity assumptions).
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Manuscript received: October 17, 2005 and, in final form, April 10, 2006.
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Aczél, J., Skof, F. Local Pexider and Cauchy equations. Aequ. math. 73, 311–320 (2007). https://doi.org/10.1007/s00010-006-2863-5
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DOI: https://doi.org/10.1007/s00010-006-2863-5