Adaptive Decomposition by Weighted Inner Functions: A Generalization of Fourier Series

In recent study adaptive decomposition of functions into basic functions of analytic instantaneous frequencies has been sought. Fourier series is a particular case of such decomposition. Adaptivity addresses certain optimal property of the decomposition. The present paper presents a fast decomposition of functions in the L 2 (@D) spaces into a series of inner and weighted inner functions of increasing frequencies.