doi: 10.7763/IJAPM.2014.V4.253
The Bijectivity of the Tight Frame Operators in Lebesgue Spaces
Kai-Cheng Wang
1
,
Chi-I. Yang
2
,
Kuei-Fang Chang
2
- 1 Ph.D. Program in Mechanical and Aeronautical Engineering, Feng-Chia University, 40724 Tai-Chung, Taiwan
- 2 Department of Applied Mathematics, Feng-Chia University, 40724 Tai-Chung, Taiwan
Abstract
The motivation of this dissertation mainly is which affine frame wavelet systems span Lebesgue spaces have been investigated less. The technique we used is analogous to technique of Calderón-Zygmund operators, but we rely on Calderón-Zygmund decomposition theorem. We prove our main results without smoothness assumption on frame wavelets. We prove that affine tight frame wavelets span Lebesgue spaces under the condition, we also show that the affine tight frame operator extends from <em>L</em><sup>2</sup>(R) to a bounded, linear and bijective operator on <em> L<sup>p</sup></em> (R) , for 1< p < . Under such condition, the affine orthonormal basis of <em>L</em><sup>2</sup>(R) is also an unconditional basis for 1< p < .
Keywords
- Bijective
- frames
- orthogonal basis
- unconditional basis
- wavelets
How to Cite
Kai-Cheng Wang, Chi-I. Yang, and Kuei-Fang Chang, "The Bijectivity of the Tight Frame Operators in Lebesgue Spaces," International Journal of Applied Physics and Mathematics, vol. 4, no. 1, pp. 46-50, 2014. https://doi.org/ 10.7763/IJAPM.2014.V4.253
Copyright & License
Copyright © 2014 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).