Re: [math-fun] Name of this transform?

I don't know, but: Why is multiplication or division by z interpreted as rotation? Or what am I missing? I thought your text meant to describe this: (Tf)(z) = i (f(z) + f(-z)) / 2 - (f(z) - f(-z)) / 2 --Dan

On Dec 18, 2014, at 10:46 AM, Mike Stay <metaweta@gmail.com> wrote:

What's the name of this transform? It basically treats the even part of the function as "real", the odd part as "imaginary", and rotates it by 90 degrees:

T(f)(z) = z even(f)(z) - odd(f)(z)/z = z(f(z) + f(-z))/2 - (f(z) - f(-z))/2z

It's somewhat related to the Hilbert transform, but that splits the function into positive and negative frequencies rather than even and odd part.