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Shift-invariant system on the Heisenberg Group
Das S.R.,
Published in Birkhauser
Volume: 6
Issue: 1
In this paper, a shift-invariant system of the form Laνgs: ν∈ Γ, s∈ Z for a> 0 is studied on the Heisenberg group Hn, where Lx denotes the left translation operator on Hn and Γ is a lattice in Hn. The characterizations for the shift-invariant system to be a Bessel sequence and a frame sequence are given in terms of certain operators arising from the fiber map corresponding to this system. For a shift invariant system to be a frame sequence (Riesz sequence) the characterization is given in terms of dual Gramian (Gramian). Moreover, the problem of characterizing a pair of shift-invariant systems to be dual frames is also discussed. © 2020, Tusi Mathematical Research Group (TMRG).
About the journal
JournalAdvances in Operator Theory
Open AccessNo