학술논문
Systems of left translates and oblique duals on the Heisenberg group.
Document Type
Article
Source
Subject
*HEISENBERG model
*LATTICE models (Statistical physics)
*RIESZ spaces
*FOURIER transforms
*WEYL groups
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Language
ISSN
2651-2939
Abstract
In this paper, we characterize the system of left translates {L(2k,l,m)g: k, l,m ∈ Z}, g ∈ L²(H), to be a frame sequence or a Riesz sequence in terms of the twisted translates of the corresponding function gλ. Here, H denotes the Heisenberg group and gλ the inverse Fourier transform of g with respect to the central variable. This type of characterization for a Riesz sequence allows us to find some concrete examples. We also study the structure of the oblique dual of the system of left translates {L(2k,l,m)g: k, l, m ∈ Z} on H. This result is also illustrated with an example. [ABSTRACT FROM AUTHOR]