Frames and semi-frames
(2011) Journal of Physics A: Mathematical and Theoretical — Vol. 44, p. 205201 (2011)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator, with bounded inverse. We study mostly upper semi-frames, both in the continuous case and in the discrete case, and give some remarks for the dual situation. In particular, we show that reconstruction is still possible in certain cases.
- Affiliations
Austrian Academy of Sciences Acoustics Research Institute
Citations
Antoine, J.-P., & Balazs, P. (2011). Frames and semi-frames. Journal of Physics A: Mathematical and Theoretical, 44, 205201. https://doi.org/10.1088/1751-8113/44/20/205201 (Original work published 2011)