Weak (quasi-)affine bi-frames for reducing subspaces of L (2)(a"e (d) )

作者：Jia HuiFang; Li YunZhang^*

来源：Science China Mathematics, 2015, 58(5): 1005-1022.

DOI：10.1007/s11425-014-4906-z

• frame
• bi-frame
• weak affine bi-frame
• weak quasi-affine bi-frame

Since a frame for a Hilbert space must be a Bessel sequence, many results on (quasi-)affine bi-frame are established under the premise that the corresponding (quasi-)affine systems are Bessel sequences. However, it is very technical to construct a (quasi-)affine Bessel sequence. Motivated by this observation, in this paper we introduce the notion of weak (quasi-)affine bi-frame (W(Q)ABF) in a general reducing subspace for which the Bessel sequence hypothesis is not needed. We obtain a characterization of WABF, and prove the equivalence between WABF and WQABF under a mild condition. This characterization is used to recover some related known results in the literature.

• 出版日期2015-5
• 单位北京工业大学