Recent content by peleg

actually... Actually... actually it is just not true; I cannot think now of an example, but it might be that f,g are analytic ONLY in (-a,a), but f+g or fg or both are analytic in a larger interval... Oh, here I have an example: take f(x) = x/(1+x), g(x) = 1/(1+x). Their sum is h(x)==1...

Well... actually, I feel a bit ignorant, but I have tried to prove that, unsuccesfuly. I have tried to use Cauchy's multiplication of series: "The product of two absolutely convergent series absolutely converges as well." - but that only proves that if f,g are analytic in (-a,a), than (fg) is...