Adaptive Decomposition by Weighted Inner Functions: A Generalization of Fourier Series

被引：24
|
作者：
Qian, Tao [1 ]
Tan, Li-Hui [2 ]
Wang, Yan-Bo [1 ]
机构：
[1] Univ Macau, Dept Math, Fac Sci & Technol, Taipa, Macao, Peoples R China
[2] Guangdong Univ Technol, Sch Appl Math, Guangzhou 510090, Guangdong, Peoples R China
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2011年 / 17卷 / 02期
关键词：
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; BEDROSIAN IDENTITY; MONO-COMPONENTS; SIGNALS; PHASE;
D O I：
10.1007/s00041-010-9154-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 L(2) (partial derivative D) spaces into a series of inner and weighted inner functions of increasing frequencies.
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页码：175 / 190
页数：16
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