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.

引用

页码：175 / 190

页数：16

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