Type: Seminar

Distribution: World

Expiry: 1 Jan 2016

Auth: leo@dyn-129-78-251-134.wirelessguest.usyd.edu.au (ltzo2369) in SMS-WASM

I will describe a constellation of results, old and new (joint with A. Vince, B. Harding, P. Viswanathan), centered around the functional equation f(x)-af(bx)=g(x), where a and b are real parameters, in various Lp spaces. The new results connect Weierstrass to fractal interpolation theory, NCG, and a remarkable orthonormal basis that reduces to {cos(nx),sin(nx)} when a=0. For a light introduction to this lecture, see http://www.anu.edu.au/news/all-news/finding-the-simple-patterns-in-a-complex-world.