Geodesic
On Parseval Wavelet Frames via Multiresolution Analyses in $H_{G}^{2}$
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 157-172

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DOI

We give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These results are based on a version of Oblique Extension Principle with the assumption that the origin is a point of approximate continuity of the Fourier transform of the involved refinable functions. Our results are written for reducing subspaces.
DOI : 10.4153/S0008439519000341
Mots-clés : dilation matrix, extension principle, Fourier transform, refinable function, tight wavelet frame 
Antolín, A. San. On Parseval Wavelet Frames via Multiresolution Analyses in $H_{G}^{2}$. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 157-172. doi: 10.4153/S0008439519000341
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     author = {Antol{\'\i}n, A. San},
     title = {On {Parseval} {Wavelet} {Frames} via {Multiresolution} {Analyses} in $H_{G}^{2}$},
     journal = {Canadian mathematical bulletin},
     pages = {157--172},
     year = {2020},
     volume = {63},
     number = {1},
     doi = {10.4153/S0008439519000341},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000341/}
}
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