Bicomplex Frames
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 3)Publication Date: 2021-08-01
Authors : Aiad Elgourari; Allal Ghanmi; Mohammed Souid El Ainin;
Page : 69-89
Keywords : Bicomplex; bc-frames; bc-frame operator; Weyl-Heisenberg bc-frame;
Abstract
We define in a natural way the bicomplex analog of the frames (bc-frames) in the setting of bicomplex infinite Hilbert spaces, and we characterize them in terms of their idempotent components. We also extend some classical results from frames theory to bc-frames and show that some of them do not remain valid for bc-frames in general. The construction of bc-frame operators and Weyl--Heisenberg bc-frames are also discussed.
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