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.
B-splines Heisenberg group Gramian Hilbert-Schmidt operator Riesz sequence moment problem oblique dual Weyl transform
Birincil Dil | İngilizce |
---|---|
Konular | Lie Grupları, Harmonik ve Fourier Analizi |
Bölüm | Makaleler |
Yazarlar | |
Erken Görünüm Tarihi | 13 Kasım 2023 |
Yayımlanma Tarihi | 15 Aralık 2023 |
Gönderilme Tarihi | 29 Ekim 2023 |
Kabul Tarihi | 9 Kasım 2023 |
Yayımlandığı Sayı | Yıl 2023 |