# Equality of two integrals

1. Aug 14, 2005

### eljose

let be the double integral:

$$\int_0^{\infty}dx\frac{f(x)}{x^{a}}\int_{-\infty}^{\infty}dyG(x+y)y^{-ib}=0 (1)$$a and b real... then we should have that:

$$\int_0^{\infty}dx\frac{f(x)}{x^{a}}\int_{-\infty}^{\infty}dyG(x+y)y^{+ib}=0$$

my question is ,let,s suppose that (2-a,b) makes also the integral (1) be zero..then my question is if necessarily 2-a=a and a=1 because we would have that:

$$\int_0^{\infty}dxf(x)(x^{-a}-x^{a-2}\int_{-\infty}^{\infty}dyG(x+y)y^{+ib}=0$$ should be zero so -a=a-2---->a=1