Toeplitz transforms of Fibonacci sequences


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2 The Catalyst Lofts, 141 41st Street, Pittsburgh, PA 15201.

3 5839 Mayflower Hill, Colby College, Waterville, ME 04901.


We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.


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