Abstract
We study decomposition of functions in the Hardy space \(H^2(\mathbb{D} )\) into linear combinations of the basic functions (modified Blaschke products) in the system
where the points a n ’s in the unit disc \(\mathbb{D}\) are adaptively chosen in relation to the function to be decomposed. The chosen points a n ’s do not necessarily satisfy the usually assumed hyperbolic non-separability condition
in the traditional studies of the system. Under the proposed procedure functions are decomposed into their intrinsic components of successively increasing non-negative analytic instantaneous frequencies, whilst fast convergence is resumed. The algorithm is considered as a variation and realization of greedy algorithm.
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Communicated by Yuesheng Xu.
The work was supported by Macao FDCT 014/2008/A1 and research grant of the University of Macau No. RG-UL/07-08s/Y1/QT/FSTR.
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Qian, T., Wang, YB. Adaptive Fourier series—a variation of greedy algorithm. Adv Comput Math 34, 279–293 (2011). https://doi.org/10.1007/s10444-010-9153-4
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DOI: https://doi.org/10.1007/s10444-010-9153-4
Keywords
- Rational orthonormal system
- Blaschke product
- Complex hardy space
- Analytic signal
- Instantaneous frequency
- Mono-components
- Adaptive decomposition of functions
- Greedy algorithm