Nonlinear phase unwinding
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We start of by studying Hardy spaces and Blaschke products. Then we look at a natural nonlinear analogue of Fourier series called the unwinding series. It is obtained through iterative Blaschke factorization and unwinds the function. We discuss the convergence of the unwinding series in various spaces and quantify how this unwinding happens. We then show that functions with some useful characteristics are close to being Hardy space functions. This can be bettered further by adding carrier frequencies which we also investigate. Then we consider decompositions of invariant subspaces of Hardy spaces and show how these relate to the unwinding series.