New results on the continuous Weinstein wavelet transform
Abstract We consider the continuous wavelet transform S h W $\mathcal{S}_{h}^{W}$ associated with the Weinstein operator. We introduce the notion of localization operators for S h W $\mathcal {S}_{h}^{W}$ . In particular, we prove the boundedness and compactness of localization operators associated...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-10-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1534-5 |
| Summary: | Abstract We consider the continuous wavelet transform S h W $\mathcal{S}_{h}^{W}$ associated with the Weinstein operator. We introduce the notion of localization operators for S h W $\mathcal {S}_{h}^{W}$ . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of S h W $\mathcal{S}_{h}^{W}$ on sets of finite measure. In particular, Benedicks-type and Donoho-Stark’s uncertainty principles are given. Finally, we prove many versions of Heisenberg-type uncertainty principles for S h W $\mathcal{S}_{h}^{W}$ . |
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| ISSN: | 1029-242X |