Year: 2020
Type: preprint
Abstract: Dynamical sampling deals with frames of the form $\{T^nφ\}_{n=0}^\infty$, where $T \in B(\mathcal{H})$ belongs to certain classes of linear operators and $φ\in\mathcal{H}$. The purpose of this paper is to investigate a new representation, namely, Fibonacci representation of sequences $\{f_n\}_{n=1}^\infty$ in a Hilbert space $\mathcal{H}$; having the form $f_{n+2}=T(f_n+f_{n+1})$ for all $n\geqslant 1$ and a linear operator $T :\text{span}\{f_n\}_{n=1}^\infty\to\text{span}\{f_n\}_{n=1}^\infty$. We apply this kind of representations for complete sequences and frames. Finally, we present some properties of Fibonacci representation operators.
Source: arXiv (Cornell University)
Authors: Moghaddam, J. Sedghi, Najati, A., Khedmati, Y.
Institution: University of Mohaghegh Ardabili
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3012763716