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A functional equation of Aczél and Chung in generalized functions. (English) Zbl 1157.39316

Summary: We consider an \(n\)-dimensional version of the functional equations of J. Aczél and J. K. Chung [Stud. Sci. Math. Hung. 17, 51–67 (1982; Zbl 0553.39005)], in the spaces of generalized functions such as the Schwartz distributions and Gelfand generalized functions. As a result, we prove that the solutions of the distributional version of the equation coincide with those of classical functional equation.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
46F10 Operations with distributions and generalized functions

Citations:

Zbl 0553.39005
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References:

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