Coherent frames. (English) Zbl 1412.42078
Summary: Frames which can be generated by the action of some operators (e.g., translation, dilation, modulation, \(\dots\)) on a single element \(f\) in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space \(\mathcal{H}\) which is indexed by some locally compact group \(G\), equipped with its left Haar measure. These frames are obtained as the orbits of a single element of Hilbert space \(\mathcal{H}\) under some unitary representation \(\pi\) of \(G\) on \(\mathcal{H}\). It is interesting that most of important frames are coherent. We investigate canonical dual and combinations of these frames.
MSC:
| 42C15 | General harmonic expansions, frames |
| 46C99 | Inner product spaces and their generalizations, Hilbert spaces |
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