论文标题
希尔伯特空间序列的斐波那契表示
Fibonacci representations of sequences in Hilbert spaces
论文作者
论文摘要
动态抽样涉及$ \ {t^nφ\} _ {n = 0}^\ infty $的框架的框架，其中$ t \ in B（\ Mathcal {h}）$属于某些类别的线性操作员和$φ\ in \ Mathcal {h} $。本文的目的是调查新的表示形式，即序列的fibonacci表示$ \ {f_n \} _ {n = 1}^\ infty $在希尔伯特space $ \ mathcal $ \ mathcal {h h} $中;具有$ f_ {n+2} = t（f_n+f_ {n+1}）$的表格$ n \ geqslant 1 $和线性运算符$ t ：\ text {span} \ {f_n \} _ {n = 1}^\ infty \ to \ text {span} \ {f_n \} _ {n = 1}^\ infty $。我们将这种表示形式应用于完整的序列和帧。最后，我们介绍了斐波那契代表操作员的一些属性。
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.
