A pair of orthogonal wavelet frames in \(L_{2}(\mathbb{R}^{d})\). (English) Zbl 1292.42020
The author gives a simple method for constructing a pair of orthogonal frames in \(L_2(\mathbb R^d)\), generalizing to high dimensions a previous result obtained for the one-dimensional case. The construction is based on the polyphase matrix and on the unitary extension principle.
Reviewer: Daniela Roşca (Cluj-Napoca)
MSC:
| 42C15 | General harmonic expansions, frames |
References:
| [1] | Bhatt G., Int. J. Math. Anal. 5 pp 2361– |
| [2] | Bhatt G., Int. J. Math. Anal. 5 pp 1583– |
| [3] | DOI: 10.1016/j.acha.2007.01.002 · Zbl 1136.42026 · doi:10.1016/j.acha.2007.01.002 |
| [4] | DOI: 10.1007/978-0-8176-8224-8 · doi:10.1007/978-0-8176-8224-8 |
| [5] | Kim O. H., J. Approx. Theory 147 |
| [6] | DOI: 10.1142/S0219691309002751 · Zbl 1157.42315 · doi:10.1142/S0219691309002751 |
| [7] | Liu Z., J. Appl. Math. 2012 |
| [8] | DOI: 10.1016/j.acha.2008.11.001 · Zbl 1171.42021 · doi:10.1016/j.acha.2008.11.001 |
| [9] | DOI: 10.1016/j.acha.2004.01.003 · Zbl 1042.42038 · doi:10.1016/j.acha.2004.01.003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
