Fa-FRAME AND RIESZ SEQUENCES IN L2(R+)

In application, L-2(R+) can model casual signal space. This paper addresses the F-a-frame theory in L-2(R+). The notion of F-a-frame for L-2(R+) is somewhat like but distinct from that of frame. One of its special cases is a dilation-and-modulation frame for L-2(R+). By intuition, F-a-frames have properties similar to usual frames. But they are nontrivial. In this paper, we introduce the notions of F-a-Bessel sequence and F-a-frame sequence in L-2(R+). We characterize F-a-Bessel sequences, frame sequences and Riesz sequences, establish the links between F-a-Bessel sequences (F-a-frame sequences) and usual Bessel sequences (frame sequences), between F-a-orthonormal sequences and Parseval F-a-frames, and obtain an expansion with respect to Parseval F-a-frame sequences.