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

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.