Nonuniform Dual Wavelets Associated with Linear Canonical Transform
محل انتشار: مجله علوم ریاضی کاسپین، دوره: 11، شماره: 2
سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 67
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شناسه ملی سند علمی:
JR_CJMS-11-2_008
تاریخ نمایه سازی: 15 اسفند 1401
چکیده مقاله:
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
کلیدواژه ها:
نویسندگان
Mohammad Bhat
Department of Mathematical sciences Islamic university of science and technology Awantipora
Aamir Dar
Department of mathematical sciences Islamic university of science and technology Awantipora