Title: Nonlinear Fourier Series via Blaschke products
Abstract: Classical Fourier Series can be generated by taking a holomorphic function and iteratively removing the value at 0 and factoring out the polynomial z. A natural nonlinear variation is to remove all the roots inside the unit disk at once. Intuitively, this should converge much faster. We discuss the arising dynamical system and prove some convergence results that are related to a classical formula of Carleson. The factorization can be carried out without actually having to find the roots thanks to an insight of Guido & Mary Weiss. This is joint work with Raphy Coifman.