Fibonacci representations of sequences in Hilbert spaces

Dynamical sampling deals with frames of the form $\{T^n\varphi\}_{n=0}^\infty$, where $T \in B(\mathcal{H})$ belongs to certain classes of linear operators and $\varphi\in\mathcal{H}$. The purpose of this paper is to investigate a new representation, namely, Fibonacci representation of sequences $\{...

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Hauptverfasser: Moghaddam, J. Sedghi, Najati, A, Khedmati, Y
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Sprache:eng
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Zusammenfassung:Dynamical sampling deals with frames of the form $\{T^n\varphi\}_{n=0}^\infty$, where $T \in B(\mathcal{H})$ belongs to certain classes of linear operators and $\varphi\in\mathcal{H}$. 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.
DOI:10.48550/arxiv.2003.09413