Toeplitz transforms of Fibonacci sequences


1 111 W. Westminster, Lake Forest, IL 60045.

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.


Main Subjects

Volume 41, Issue 7 (Special Issue)
December 2015
Pages 123-132
  • Receive Date: 28 April 2015
  • Revise Date: 28 June 2015
  • Accept Date: 28 June 2015
  • First Publish Date: 01 December 2015