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Adaptive Fourier decomposition in H p
Author(s) -
Wang Yanbo,
Qian Tao
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5494
Subject(s) - mathematics , normalization (sociology) , decomposition , norm (philosophy) , fourier transform , fourier series , convergence (economics) , pure mathematics , algorithm , mathematical analysis , ecology , sociology , anthropology , political science , law , economics , biology , economic growth
In this paper, we study decomposition of functions in Hardy spaces H p ( T ) ( 1 < p < ∞ ) . First, we will give a direct application of adaptive Fourier decomposition (AFD) of H 2 ( T ) to functions in H p ( T ) . Then, we study adaptive decomposition by the system 1 D : =e a ( z ) =A a , p1 − ā z , a ∈ D , where A a , p is the normalization factor making e a ( z ) to be of unit p ‐norm. Under the proposed decomposition procedure, we show that every f ∈ H p ( T ) can be effectively expressed by a linear combination of{ ea n( z ) } n = 1 + ∞ . We give a maximal selection principle ofea nat the n th step and prove the convergence.