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g-Besselian frames in Hilbert spaces. (English) Zbl 1209.42028
Summary: We introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.
42C99Non-trigonometric Fourier analysis
42C25Uniqueness and localization for orthogonal series
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