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adaptive decomposition by Weighted Inner functions: A Generalization of Fourier Series

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 2011年第2期17卷 175-190页

作者： Qian, Tao Tan, Li-Hui Wang, Yan-Bo Univ Macau Dept Math Fac Sci & Technol Taipa Macao Peoples R China Guangdong Univ Technol Sch Appl Math Guangzhou 510090 Guangdong Peoples R China

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.

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

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Intrinsic mono-component decomposition of functions: An advance of Fourier theory

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2010年第7期33卷 880-891页

作者： Qian, Tao Univ Macau Dept Math Fac Sci & Technol Taipa Macao Peoples R China

We propose a function decomposition model, called intrinsic mono-component decomposition (IMD). It is a continuation of the recent study on adaptive decomposition of functions into mono-components (MCs). It is a further improvement of two recent results of which one is adaptive decomposition of functions into modified inner functions, and the other is decomposition by using adaptive Takenaka-Malmquist systems. The proposed new decomposition model is of less restriction and thus gains more adaptivity. The theory is valid to both the unit circle and the real line contexts. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： complex hardy space inner and outer functions Nevanlinna factorization theorem Takenaka-Malmquist system analytic signal instantaneous frequency and amplitude mono-components Greedy algorithm adaptive decomposition of functions

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adaptive Fourier series-a variation of greedy algorithm

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2011年第3期34卷 279-293页

作者： Qian, Tao Wang, Yan-Bo Univ Macau Dept Math Fac Sci & Technol Taipa Peoples R China

The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with It's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations. The existence and uniqueness results of the general FBSDEs are obtained. In the framework of the general FBSDEs in this paper, the explicit form of the optimal control for linearquadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.

关键词： Rational orthonormal system Blaschke product Complex hardy space Analytic signal Instantaneous frequency Mono-components adaptive decomposition of functions Greedy algorithm

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