2015/05/14 by Bouikhalene Belaid, Belaid, Bouikhalene, Elqorachi Elhoucien +1
Mathematics · #39B32 #39B52 #39B82 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:39B32 #msc:39B52 #msc:39B82
paper · pdf · doi:10.48550/arxiv.1505.06513
12pages
arxiv created 2015/05/14 · arxiv updated 2015/05/26
In this paper we study the solutions and stability of the generalized Wilson's functional equation ∫Gf(xty)dμ(t)+∫Gf(xtσ(y))dμ(t)=2f(x)g(y), x,y∈ G, where G is a locally compact group, σ is a continuous involution of G and μ is an idempotent complex measure with compact support and which is σ-invariant. We show that ∫Gg(xty)dμ(t)+∫Gg(xtσ(y))dμ(t)=2g(x)g(y), x,y∈ G if f≠ 0 and ∫Gf(t.)dμ(t)≠ 0. We also study some stability theorems of that equation and we establish the stability on noncommutaive groups of the classical Wilson's functional equation f(xy)+χ(y)f(xσ(y))=2f(x)g(y) x,y∈ G, where χ is a unitary character of G.