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A Research on Perturbations of Bessel Sequences and Normalized Windowed Fourier Transformation

Author: LiuQin
Tutor: CaoHuaiXin
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: Hilbert space Bessel column Generalized disturbance Operator perturbation Specification window Fourier transform Strong inversion formula
CLC: O177.1
Type: Master's thesis
Year: 2010
Downloads: 21
Quote: 0
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Abstract


The theoretical framework wavelet analysis Bessel column is defined framework .1952 Duffin and Schaeffer to promote the idea of the Gabor and the first to propose the framework of the concept in the Hilbert space . Thereafter , the framework of the theory has caused many scholars widespread concern in recent years, it has been systematically studied . Bessel column Hilbert space , framework and theory of Riesz basis to overcome many of the shortcomings of the traditional Fourier transform , Gabor was proposed in 1946 and uses the concept of a windowed Fourier transform it is an important time-frequency analysis tools . article discusses the generalized Bessel column Hilbert space disturbances and operator perturbations specification window Fourier transform strong inversion formula and important nature . text is divided into three chapters , each chapter the main contents are as follows : the first chapter introduces the research background and research status of wavelet analysis , and a brief description of the organization of some major work of this article and this article . chapter first introduces the basic framework of the theory in the Hilbert space , and then discuss the Hilbert generalized disturbance of the the Bessel column space to discuss the stability after the the original Bessel column generalized disturbance by defining new sequence that is in the original Bessel column add new elements , add a column and then give the new coefficients constitute a new the sequence paper gives a new sequence to become the Bessel columns to meet the conditions . simultaneously to a large number of examples to prove the existence of such perturbations . then by analogy Finally the Bessel operator column disturbance . upcoming generalized perturbation new coefficient , instead of a series of linear operator role in every one to form a new sequence , the article gives a new sequence conditions for Bessel column . third chapter use functional theory , through the specification window Fourier transform Twwin f is defined as a sequence of functions { Fn } n = 1 ∞ and prove that it is the norm in L2 (R) converges to f , resulting in a strong inversion formula specification window Fourier transform .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Hilbert space and linear operator theory
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