Smooth Functions Associated with Wavelet Sets on Rd, d ≥ 1, and Frame Bound Gaps

被引：3

作者：

Benedetto, John J. ^{[2
]}

King, Emily J. ^{[1
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ Maryland, Norbert Wiener Ctr, College Pk, MD 20742 USA

来源：

ACTA APPLICANDAE MATHEMATICAE | 2009年 / 107卷 / 1-3期

关键词：

Wavelet sets; Frames; Convolutional smoothing; Frame bound gaps; SINGLE WAVELETS; PERTURBATIONS; CONSTRUCTION; STABILITY;

D O I：

10.1007/s10440-008-9412-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theme is to smooth characteristic functions of Parseval frame wavelet sets by convolution in order to obtain implementable, computationally viable, smooth wavelet frames. We introduce the following: a new method to improve frame bound estimation; a shrinking technique to construct frames; and a nascent theory concerning frame bound gaps. The phenomenon of a frame bound gap occurs when certain sequences of functions, converging in L-2 to a Parseval frame wavelet, generate systems with frame bounds that are uniformly bounded away from 1. We prove that smoothing a Parseval frame wavelet set wavelet on the frequency domain by convolution with elements of an approximate identity produces a frame bound gap. Furthermore, the frame bound gap for such frame wavelets in L-2( R-d) increases and converges as d increases.

引用

页码：121 / 142

页数：22

共 39 条

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