Phase unwinding, or invariant subspace decompositions of Hardy spaces

Abstract: We consider orthogonal decompositions of invariant subspaces of Hardy spaces, these relate to the Blaschke based phase unwinding decompositions. We prove convergence in Lp. In particular we build an explicit multiscale wavelet basis. We also obtain an explicit unwindinig decomposition for the singular inner function, exp 2i\pi/x.