Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces. (6th April 2015) - Guo, Xunxiang
Abstract : Firstly, we study the representation ofg -frames in terms of linear combinations of simpler ones such asg -orthonormal bases, g -Riesz bases, and normalized tightg -frames. Then, we study the dual and pseudodual ofg -frames, which are critical components in reconstructions. In particular, we characterize the dualg -frames in a constructive way; that is, the formulae for dualg -frames are given. We also give someg -frame like representations for pseudodualg -frame pairs. The operator parameterizations ofg -frames and decompositions of bounded operators are the key tools to prove our main results.