Askari Hemmat, A., Safapour, A., Yazdani Fard, Z. (2018). Coherent Frames. Sahand Communications in Mathematical Analysis, 11(1), 1-11. doi: 10.22130/scma.2018.68276.261

Askari Hemmat, A., Safapour, A., Yazdani Fard, Z. (2018). 'Coherent Frames', Sahand Communications in Mathematical Analysis, 11(1), pp. 1-11. doi: 10.22130/scma.2018.68276.261

Askari Hemmat, A., Safapour, A., Yazdani Fard, Z. Coherent Frames. Sahand Communications in Mathematical Analysis, 2018; 11(1): 1-11. doi: 10.22130/scma.2018.68276.261

^{1}Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.

^{2}Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.

Abstract

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) 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 this frames

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