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arXiv · 1101.2859

Frames and Semi-Frames

Jean-Pierre Antoine·Peter Balazs
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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.

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Jean-Pierre Antoine, Peter Balazs. 2011-04-18. Frames and Semi-Frames. https://doi.org/10.1088/1751-8113/44/20/205201

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