Wenchang Sun
Stability of G-frames
Preprint series: ESI preprints

MSC:

42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

Abstract: G-frames are natural generalizations of frames
which cover many other recent generalizations of frames,
e.g., bounded quasi-projectors, frames of subspaces,
outer frames, oblique frames, pseudo-frames
and a class of time-frequency localization operators.
Moreover, it was shown that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We
first present some properties for g-Bessel sequences.
Then we prove that g-frames are stable under small perturbations.
We also study the stability of dual g-frames.

Keywords: G-frames, generalized frames, stability