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Antoine, Jean-Pierre; Balazs, Peter (2011)
Languages: English
Types: Article
Subjects: Gabor frames, Mathematical Physics, Semi-frames, Mathematics - Functional Analysis, 42C15, 42C40, 65T60, Unbounded frames, Bessel sequences
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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    • [37] Weidmann J 1980 Linear Operators in Hilbert Spaces (New York, Heidelberg, Berlin: Springer)
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