Frames and semi-frames in mathematical physics
(2013) Contemporary Problems in Mathematical Physics (Proc. Seventh Int. Workshop) — 48-58, published
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- Authors
Antoine, Jean-Pierre 
- Abstract
- Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if the sequence satisfies only the upper (resp. lower) frame bound. 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. Both concepts are extended to the continuous case. For upper semi-frames, in the discrete and the continuous case, we build two natural Hilbert scales which may yield a novel characterization of certain function spaces of interest in signal processing or mathematical physics. We present some results concerning the duality between lower and upper semi-frames, as well as two examples involving wavelets/coherent states.
- Affiliations
Citations
Antoine, J.-P. (2013). Frames and semi-frames in mathematical physics. In J. Govaerts and M.N.Hounkonnou (eds.) (ed.), Contemporary Problems in Mathematical Physics (Proc. Seventh Int. Workshop) (pp. 48-58). ICMPA Publishing. https://hdl.handle.net/2078.5/28380