摘要
We show that every Bessel sequence （and therefore every frame） in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concept, the g-frame, which illustrates that g-frames could be useful in the study of frame theory. As an application, we prove that any Gabor frame can be expanded to a tight frame by adding one window function.
We show that every Bessel sequence （and therefore every frame） in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concept, the g-frame, which illustrates that g-frames could be useful in the study of frame theory. As an application, we prove that any Gabor frame can be expanded to a tight frame by adding one window function.
基金
supported partially by the National Natural Science Foundation of China (10571089,10671062)
the Program for New Century Excellent Talents in Universities
the Innovation Scientists and Technicians Troop Construction Projects of He'nan Province of China (084100510012)
the Natural Science Foundation for the Education Department of He'nan Province of China (2008B510001)
