Recent content by emra1976

Now, given $$f(z)=\frac{cos(\omega z)}{1+\omega z}$$ how would you choose the contour for the Cauchy Integral? My two choices would be 1) the quarter disk in the top right quadrant of the complex plane 2) a rectangular contour in the top right quadrant of the complex plane but I get...

Do you mean that $$\frac{1}{1+|z|}$$ is not analytical (used as homomorphic)? If so, where are its poles?

1) it should be $$f(x)=\frac{1}{1+\abs{x}}$$ 2) I tried Cauchy theorem using the fact that $$f(z)=\frac{1}{1+\abs{z}}$$ is analytical. I tried both the rectangular contour $$([-R,R],[R,R+ip],[R+ip,-R+ip],[-R+ip,-R])$$ and the the countour of the semidisk centered on the origin with radius $$R$$.

Yes, you are correct. While I need to generalise it to x\in\mathbb{R}^n I would like to start with the case in which x\in \mathbb{R} and \norm{x}=\abs{x}

Homework Statement Compute the Fourier transform of a function of norm f(\norm{x}). Homework Equations \mathbb{F}{\frac{1}{1+\norm{x}} The Attempt at a Solution Attempt at using Cauchy theorem and the contour integral with the contour [(-R,R),(R,R+ip),(R+ip,-R+ip),(-R+ip,-R)] does...