Advertisement

Products of Daubechies Operators

  • M. W. Wong
Part of the Operator Theory: Advances and Applications book series (OT, volume 136)

Abstract

Let FL 2(ℂ n and let ϕ ∈ L 2(ℝ n be such that \(\parallel \varphi {{\parallel }_{{{{L}^{2}}({{\mathbb{R}}^{n}})}}} = 1\). Then the Daubechies operator associated to the symbol F and the admissible wavelet (p is the bounded linear operator \({{D}_{{F,\varphi }}}:{{L}^{2}}({{\mathbb{R}}^{n}}) \to {{L}^{2}}({{\mathbb{R}}^{n}})\) defined by (17.23) for all functions f and g in L 2(ℝ n . We give in this chapter a formula for the product of two Daubechies operators when the admissible wavelet ϕ is chosen to be the function given by
$$\begin{array}{*{20}{c}} {\varphi (x) = {{\pi }^{{ - \tfrac{n}{4}}}}{{e}^{{ - \tfrac{{|x{{|}^{2}}}}{2}}}},} & {x \in {{\mathbb{R}}^{n}}.} \\ \end{array}$$
(22.1)
The starting point is the following theorem.

Keywords

Real Number Positive Constant Linear Operator Characteristic Function Measurable Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • M. W. Wong
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

Personalised recommendations