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Invariances of frame sequences under perturbations |
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| Authors: | Shannon Bishop Christopher Heil Yoo Young Koo Jae Kun Lim |
| Institution: | a School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA b Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea c Department of Applied Mathematics, Hankyong National University, 67 Seokjeong-dong Anseong-si, Gyeonggi-do 456-749, Republic of Korea |
| Abstract: | This paper determines the exact relationships that hold among the major Paley-Wiener perturbation theorems for frame sequences. It is shown that major properties of a frame sequence such as excess, deficit, and rank remain invariant under Paley-Wiener perturbations, but need not be preserved by compact perturbations. For localized frames, which are frames with additional structure, it is shown that the frame measure function is also preserved by Paley-Wiener perturbations. |
| Keywords: | 42C15 46C99 |
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