Coherent Frames

Sahand Communications in Mathematical Analysis

Ahmad Safapour¹  Zohreh Yazdani Fard¹  Ataollah Askari Hemmat² 

[1] Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.;Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.;

关键词: Coherent frame;    Continuous frame;    Locally compact group;    Unitary representation;   

DOI  :  10.22130/scma.2018.68276.261

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown