| Hyers-Ulam stability of Wilson functional equation, that is, the generalized d'Alembert functional equation are mainly studied in the paper. Firstly, by used the unbounded-ness of functions, the stability of Wilson functional equation is obtained in the space of continuous functions. And then using heat kernel and the approach of regularizing generalized functions, stability of Wilson functional equation is given in the spaces of generalized functions such as the Schwartz tempered distributions, Fourier hyperfunc-tions and Gelfand-shilov generalized functions.
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