Properties of oblique dual frames in shift-invariant systems |
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| Authors: | A. Askari Hemmat Jean-Pierre Gabardo |
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| Affiliation: | a Department of Mathematics, Shahid Bahonar University of Kerman, 22 Bahman blv., Kerman, Iran
b Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada |
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| Abstract: | Gramian analysis is used to study properties of a shift-invariant system  , where B is an invertible n×n matrix and Φ a finite or countable subset of L2(Rn) under the assumption that the system forms a frame for the closed subspace M of L2(Rn). In particular, the relationship between various features of such system, such as being a frame for the whole space L2(Rn), being a Riesz sequence and having a unique shift-generated dual of type I or II is discussed in details. Several interesting examples are presented. |
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| Keywords: | Shift invariant spaces Dual frames Dual of type I and type II Gramian matrix Gramian operator |
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