近似对偶g-框架的刻画

    Characterization of Approximate Dual g-frame

    • 摘要: 近似对偶框架的构造比经典对偶框架的构造更为容易,而且可以导出几乎同样完美的重构公式,在子空间框架(fusion框架)的背景下,给出了近似对偶g-框架的明确刻画.作为应用,证明了对于给定的一组近似对偶g-框架(ΛnnΓnn),存在另一组近似对偶框架(ΨnnΥnn),使得TΛUΓ=TΨUΥ,其中TYUY分别表示g-框架Ynn的准框架算子与分析算子.

       

      Abstract: Constructing approximate dual frames is much easier than constructing classical dual frames, and approximate dual frames derive an almost same perfect reconstruction formula as classical dual frames. In this paper, under the background of subspace frames (fusion frames), an explicit characterization of approximate dual g-frames was obtained. As an application, we prove that for a given pair of approximate dual g-frames (Λnn, Γnn), there existed another pair of approximate dual g-frames (Ψnn, Υnn) such that TΛUΓ=TΨUΥ, where TY and UY denote the pre-frame and analysis operators of the g-frame Ynn.

       

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