Wavelet frames and admissibility in higher dimensions
- 1 December 1996
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 37 (12), 6353-6366
- https://doi.org/10.1063/1.531752
Abstract
This paper is concerned with the relations between discrete and continuous wavelet transforms on k-dimensional Euclidean space. We start with the construction of continuous wavelet transforms with the help of square-integrable representations of certain semidirect products, thereby generalizing results of Bernier and Taylor. We then turn to frames of L2(Rk) and to the question, when the functions occurring in a given frame are admissible for a given continuous wavelet transform. For certain frames we give a characterization which generalizes a result of Daubechies to higher dimensions.Keywords
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