臺灣博碩士論文加值系統

在這篇論文裡，我們首先介紹一些有關基底、正交基底、frame和多層解析空間（MRA）的基本架構。接著，如果自格函數構成一個多層解析空間的話，那我們可以去證明在某些條件之下自格函數的積分不會等於零。最後，在小波分析裡，我們對於小波函數有消散動差，給一些充分條件。

In this thesis, firstly, we introduce several fundamental notions about orthonormal bases, Riesz bases and frames. Subsequently, if a scaling function generates a multiresolution analysis（MRA）, under some conditions we can prove that the integral of the scaling function is nonzero. Finally, in wavelet analysis, we give some necessary conditions that a wavelet function has vanishing moments.

1.Introduction...........................................2

2.Fundamental Notions for Bases and Frames...............4

3.Multiresolution Analysis...............................16

4.Fundamentality in L2(R)................................22

5.Vanishing Moments......................................26

6.Future Work............................................35

7.Reference..............................................36

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