Fibonacci representations of sequences in Hilbert spaces
Abstract
Dynamical sampling deals with frames of the form \Tn\n=0∞, where T ∈ B(H) belongs to certain classes of linear operators and ∈H. The purpose of this paper is to investigate a new representation, namely, Fibonacci representation of sequences \fn\n=1∞ in a Hilbert space H; having the form fn+2=T(fn+fn+1) for all n≥slant 1 and a linear operator T :span\fn\n=1∞\fn\n=1∞. We apply this kind of representations for complete sequences and frames. Finally, we present some properties of Fibonacci representation operators.
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