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Volume 34, Issue 2
On Characterization of Nonuniform Tight Wavelet Frames on Local Fields

Owais Ahmad & Neyaz A. Sheikh

DOI: 10.4208/ata.2018.v34.n2.4

Anal. Theory Appl., 34 (2018), pp. 135-146.

Published online: 2018-07

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  • Abstract

In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.

  • Keywords

Nonuniform wavelet frame, tight wavelet frame, Fourier transform, local field.

  • AMS Subject Headings

43A70, 11S85, 42C40, 42C15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-34-135, author = {Owais Ahmad and Neyaz A. Sheikh}, title = {On Characterization of Nonuniform Tight Wavelet Frames on Local Fields}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {2}, pages = {135--146}, abstract = {

In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2018.v34.n2.4}, url = {http://global-sci.org/intro/article_detail/ata/12582.html} }
TY - JOUR T1 - On Characterization of Nonuniform Tight Wavelet Frames on Local Fields AU - Owais Ahmad & Neyaz A. Sheikh JO - Analysis in Theory and Applications VL - 2 SP - 135 EP - 146 PY - 2018 DA - 2018/07 SN - 34 DO - http://doi.org/10.4208/ata.2018.v34.n2.4 UR - https://global-sci.org/intro/article_detail/ata/12582.html KW - Nonuniform wavelet frame, tight wavelet frame, Fourier transform, local field. AB -

In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.

Owais Ahmad and Neyaz A. Sheikh. (2018). On Characterization of Nonuniform Tight Wavelet Frames on Local Fields. Analysis in Theory and Applications. 34 (2). 135-146. doi:10.4208/ata.2018.v34.n2.4
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