Abstract
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 \(\mathcal {L}^{2}(\partial {\mathbb{D}})\) spaces into a series of inner and weighted inner functions of increasing frequencies.
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Communicated by Patrick Flandrin.
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., Tan, LH. & Wang, YB. Adaptive Decomposition by Weighted Inner Functions: A Generalization of Fourier Series. J Fourier Anal Appl 17, 175–190 (2011). https://doi.org/10.1007/s00041-010-9154-1
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DOI: https://doi.org/10.1007/s00041-010-9154-1
Keywords
- Fourier series
- Inner and outer functions
- Hardy space
- The Nevanlinna factorization theorem
- Blaschke product
- Analytic signal
- Instantaneous frequency and amplitude
- Mono-components
- Adaptive decomposition of functions