Inequalities for nonuniform wavelet frames
Keyword(s):
Abstract Gabardo and Nashed studied nonuniform wavelets by using the theory of spectral pairs for which the translation set {\Lambda=\{0,r/N\}+2\mathbb{Z}} is no longer a discrete subgroup of {\mathbb{R}} but a spectrum associated with a certain one-dimensional spectral pair. In this paper, we establish three sufficient conditions for the nonuniform wavelet system {\{\psi_{j,\lambda}(x)=(2N)^{j/2}\psi((2N)^{j}x-\lambda),\,j\in\mathbb{Z},\,% \lambda\in\Lambda\}} to be a frame for {L^{2}(\mathbb{R})} . The proposed inequalities are stated in terms of Fourier transforms and hold without any decay assumptions on the generator of such a system.
Keyword(s):
2018 ◽
Vol 10
(2)
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pp. 340-346
2020 ◽
Vol 74
(2)
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pp. 1
Keyword(s):
Keyword(s):
2020 ◽
Vol 18
(03)
◽
pp. 2050009
2018 ◽
Vol 16
(01)
◽
pp. 1850005
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