Weak (quasi-)affine bi-frames for reducing subspaces of \(L^{2}(\mathbb{R}^{d})\) (Q2516914)

Since frames are Bessel sequences, many results on (quasi-)affine bi-frames are established by using the fact that the corresponding (quasi-)affine systems are Bessel sequences. However, constructing Bessel sequences can be technical. The paper introduces the notion of a weak (quasi-)affine bi-frame in a general reducing subspace. Using this notion, one can avoid dealing with Bessel sequences. The paper also provides a characterization of weak affine bi-frames and establishes an equivalence between weak affine bi-frames and weak (quasi-)affine bi-frames.