Is This Integral a Candidate for Asymptotic Analysis?

[thrillhouse86]

Hey:

I have an integral of the form:
<br /> \int^{\infty}_{-\infty}\frac{x(\omega)}{\sigma^{2} + \omega^{2}}d\omega<br />

I'm wondering if this integral is a candidate for asymptotic analysis. My rationale is that as omega increases to either positive infinity or negative infinity, the function being integrated will go to zero. The problem is that every integral I've seen put into an Asymptotic form has had a decaying exponential (which I guess is a much quicker convergence to zero than 1/w^2).

Also - I can guarantee that any f(w) considered is square integrable, and sigma is real

I realize that I can probably just evaluate the integral using contour methods if I have a specific f(w), but I am trying to derive the most general result I can.

I guesss my question is:
1. Is this a candidate for asymptotic analysis
2. If so can someone point me in the direction of obtaining the asymptotic form ?

Thanks

 

[fresh_42]

Without any knowledge about $x(\omega)$ the integral could be anything.