Abstract

In this paper, we study decomposition of functions in Hardy spaces . First, we will give a direct application of adaptive Fourier decomposition (AFD) of to functions in . Then, we study adaptive decomposition by the system urn:x-wiley:mma:media:mma5494:mma5494-math-0007 where Aa,p is the normalization factor making ea(z) to be of unit p‐norm. Under the proposed decomposition procedure, we show that every can be effectively expressed by a linear combination of . We give a maximal selection principle of at the nth step and prove the convergence.

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