TY  - JOUR
T1  - Systems of left translates and oblique duals on the Heisenberg group
AU  - Massopust, Peter
AU  - Das, Santi
AU  - Ramakrishnan, Radha
PY  - 2023
DA  - December
Y2  - 2023
DO  - 10.33205/cma.1382306
JF  - Constructive Mathematical Analysis
JO  - CMA
PB  - Tuncer ACAR
WT  - DergiPark
SN  - 2651-2939
SP  - 222
EP  - 236
VL  - 6
IS  - 4
LA  - en
AB  - In this paper, we characterize the system of left translates $\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$, $g\in L^2(\mathbb{H})$, to be a frame sequence or a Riesz sequence in terms of the twisted translates of the corresponding function $g^\lambda$. Here, $\mathbb{H}$ denotes the Heisenberg group and $g^\lambda$ 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 $\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$ on $\mathbb{H}$. This result is also illustrated with an example.
KW  - B-splines
KW  - Heisenberg group
KW  - Gramian
KW  - Hilbert-Schmidt operator
KW  - Riesz sequence
KW  - moment problem
KW  - oblique dual
KW  - Weyl transform
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UR  - https://doi.org/10.33205/cma.1382306
L1  - https://dergipark.org.tr/en/download/article-file/3501161
ER  -