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Nonuniform Dual Wavelets Associated with Linear Canonical Transform | ||
| Caspian Journal of Mathematical Sciences (CJMS) | ||
| دوره 11، شماره 2، اسفند 2022، صفحه 461-479 اصل مقاله (427.53 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2022.21790.1588 | ||
| نویسندگان | ||
| Mohammad Younus Bhat* 1؛ Aamir H Dar2 | ||
| 1Department of Mathematical sciences Islamic university of science and technology Awantipora | ||
| 2Department of mathematical sciences Islamic university of science and technology Awantipora | ||
| تاریخ دریافت: 28 خرداد 1400، تاریخ بازنگری: 20 مرداد 1400، تاریخ پذیرش: 04 شهریور 1400 | ||
| چکیده | ||
| A generalization of Mallat’s classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set is no longer a discrete subgroup of R but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we are interested in the dual wavelets whose construction depends on nonuniform multiresolution analysis associated with linear canonical transform. Here we prove that if the translates of the scaling functions of two multiresolution analyses in linear canonical transform settings are biorthogonal, so are the wavelet families which are associated with them. Under mild assumptions on the scaling functions and the wavelets, we also show that the wavelets generate Riesz bases | ||
| کلیدواژه‌ها | ||
| Nonuniform؛ Biorthogonal؛ Scaling function؛ Linear Canonical Transform | ||
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آمار تعداد مشاهده مقاله: 136 تعداد دریافت فایل اصل مقاله: 81 |
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