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- Title
Adaptive Fourier decomposition in Hp.
- Authors
Wang, Yanbo; Qian, Tao
- Abstract
In this paper, we study decomposition of functions in Hardy spaces Hp(T)(1<p<∞). First, we will give a direct application of adaptive Fourier decomposition (AFD) of H2(T) to functions in Hp(T). Then, we study adaptive decomposition by the system 1D:=ea(z)=Aa,p1−āz,a∈D,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 f∈Hp(T) can be effectively expressed by a linear combination of {ean(z)}n=1+∞. We give a maximal selection principle of ean at the nth step and prove the convergence.
- Subjects
HARDY spaces; TECHNOLOGY convergence; FUNCTION spaces
- Publication
Mathematical Methods in the Applied Sciences, 2019, Vol 42, Issue 6, p2016
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.5494