关键词: Wilson函数方程； 广义函数； 热方程的核； HyersUlam稳定性

Abstract:

By means of heat kernel and the approach of regularizing generalized functions, HyersUlam stability of Wilson functional equation was
 mainly studied in the spaces of generalized functions such as the Schwartz tempered distributions, Fourier hyperfunctions and Gelfandshilov generalized functions, showing that the result of the stability of Wilson functional equation in generalized functions is similar to that in the usual functional spaces.

Key words: Wilson functional equation； generalized functions； heat kernel； HyersUlam stability