2011/01/31 by Jean-Pierre Antoine, Peter Balazs · 2 citations
Mathematics · Physics and Astronomy · #math.FA #math-ph #math.MP #msc:42C15 #msc:42C40 #msc:65T60
paper · pdf · doi:10.1088/1751-8113/44/20/205201
published as J. Phys. A: Math. Theor. 44 205201 (2011) · 25 pages
arxiv created 2011/04/18 · arxiv updated 2012/05/31
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.