| Morteza RAHMANI.On Some Properties of $c$-Frames[J].数学研究及应用,2017,37(4):466~476 |
| On Some Properties of $c$-Frames |
| On Some Properties of $c$-Frames |
| 投稿时间：2016-04-30 修订日期：2017-03-29 |
| DOI：10.3770/j.issn:2095-2651.2017.04.008 |
| 中文关键词: Banach space Hilbert space frame $c$-frame Parseval $c$-frame Bochner measurable |
| 英文关键词:Banach space Hilbert space frame $c$-frame Parseval $c$-frame Bochner measurable |
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| 中文摘要: |
| In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames. |
| 英文摘要: |
| In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames. |
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