Intrinsic mono-component decomposition of functions: An advance of Fourier theory

摘要

We propose a function decomposition model, called intrinsic mono-component decomposition (IMD). It is a continuation of the recent study on adaptive decomposition of functions into mono-components (MCs). It is a further improvement of two recent results of which one is adaptive decomposition of functions into modified inner functions, and the other is decomposition by using adaptive Takenaka-Malmquist systems. The proposed new decomposition model is of less restriction and thus gains more adaptivity. The theory is valid to both the unit circle and the real line contexts.