Approximately dual and perturbation results for generalized translation-invariant frames on LCA groups
2018 ◽
Vol 16
(03)
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pp. 1850017
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Keyword(s):
The Real
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The results in this paper can be divided into three parts. First, we generalize the recent results of Benavente, Christensen and Zakowicz on approximately dual generalized shift-invariant frames on the real line to generalized translation-invariant (GTI) systems on locally compact abelian (LCA) groups. Second, we explain in detail how GTI frames can be realized as [Formula: see text]-frames. Finally, the known results on perturbation of [Formula: see text]-frames and results on perturbation of generalized shift-invariant systems are applied and extended to GTI systems on LCA groups.
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups
2016 ◽
Vol 368
(12)
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pp. 8447-8480
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2016 ◽
Vol 437
(1)
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pp. 590-604
1987 ◽
Vol 10
(3)
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pp. 461-471
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