Perturbations of the Haar wavelet期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Perturbations of the Haar wavelet

Authors:	N K Govil R A Zalik

Institution:	Department of Mathematics, Auburn University, Auburn, Alabama 36849--5310 ; Department of Mathematics, Auburn University, Auburn, Alabama 36849--5310

Abstract:	Let $m \in Z^+$ be given. For any $\varepsilon > 0$ we construct a function $f^{\{\varepsilon \}}$ having the following properties: (a) $f^{\{\varepsilon \}}$ has support in $-\varepsilon , 1 + \varepsilon ]$ . (b) $f^{\{\varepsilon \}} \in C^m(-\infty , \infty )$ . (c) If denotes the Haar function and $0<\delta <\infty$ , then $\Vert f^{\{\varepsilon \}} - h \Vert _{L^\delta (\mathcal R)} \le (1+2^\delta )^{1/\delta }(2\varepsilon )^{1/\delta }$ . (d) $f^{\{\varepsilon \}}$ generates an affine Riesz basis whose frame bounds (which are given explicitly) converge to as $\varepsilon \rightarrow 0$ .

Keywords:	Frames affine frames Riesz bases Haar wavelet basis perturbations $\wedge$-bounded mean variation cardinal splines

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