Positive Weight Function and Classification of g-Frames
Abstract
Given a positive weight function and an isometry map on a Hilbert spaces $\mathcal{H}$, we study a class of linear maps which is a $g$-frame, $g$-Riesz basis and a $g$-orthonormal basis for $\mathcal{H}$ with respect to $\mathbb{C}$ in terms of the weight function. We apply our results to study the frame for shift-invariant subspaces on the Heisenberg group.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- 10.48550/arXiv.1902.09282
- arXiv:
- arXiv:1902.09282
- Bibcode:
- 2019arXiv190209282P
- Keywords:
-
- Mathematics - Functional Analysis;
- 42C15;
- 43A80
- E-Print:
- Numer. Funct. Anal. Optim. 41(8): 950-968 (2020)