Analysis and its Applications Seminar
Homeomorphisms of a circle and factorization
For each n > 0 there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations `conjugated by z -> z^n'. In this talk I will discuss a number of analytic issues which arise in trying to factor a general homeomorphism in terms of these basic building blocks. This is an attempt to develop a nonlinear version of Fourier series in which addition is replaced by composition.