Abstract and Applied Analysis

Characterization of Generators for Multiresolution Analyses with Composite Dilations

Abstract

This paper introduces multiresolution analyses with composite dilations (AB-MRAs) and addresses frame multiresolution analyses with composite dilations in the setting of reducing subspaces of ${L}^{2}({\mathbb{N}}^{n})$ (AB-RMRAs). We prove that an AB-MRA can induce an AB-RMRA on a given reducing subspace ${L}^{2}{(S)}^{\vee }$. For a general expansive matrix, we obtain the characterizations for a scaling function to generate an AB-RMRA, and the main theorems generalize the classical results. Finally, some examples are provided to illustrate the general theory.

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 850850, 13 pages.

Dates
First available in Project Euclid: 12 August 2011

https://projecteuclid.org/euclid.aaa/1313171134

Digital Object Identifier
doi:10.1155/2011/850850

Mathematical Reviews number (MathSciNet)
MR2784387

Zentralblatt MATH identifier
1211.42037

Citation

Zhu, Yuan; Gao, Wenjun; Li, Dengfeng. Characterization of Generators for Multiresolution Analyses with Composite Dilations. Abstr. Appl. Anal. 2011 (2011), Article ID 850850, 13 pages. doi:10.1155/2011/850850. https://projecteuclid.org/euclid.aaa/1313171134