摘要
In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.
In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.
