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

On Thu, Dec 18, 2014 at 12:25 PM, Daniel Asimov <asimov@msri.org> wrote:

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

No. Assume f is continuously differentiable so it has a Taylor series. This transform swaps neighboring coefficients in the Taylor series and negates one of them. Split f into even and odd parts fe and fo. Think of f as a 2-d vector |fe| |fo| Then rotate via the matrix |0 -1| |1 0| which is like i in that applying the matrix twice is minus the identity. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com