|
Title:
|
The Spectrum of the Off-diagonal
Fibonacci Operator |
|
Author:
|
Dahl, Janine |
|
Advisor:
|
David Damanik |
|
Degree:
|
Doctor of Philosophy thesis |
|
Abstract:
|
The family of off-diagonal Fibonacci operators can be considered as Jacobi matrices
acting in .e2(Z) with diagonal entries zero and off-diagonal entries given by
sequences in the hull of the Fibonacci substitution sequence. The spectrum is independent
of the sequence chosen and thus the same for all operators in the family.
The spectrum is purely singular continuous and has Lebesgue measure zero. We will
consider the trace map and its relation to the spectrum. Upper and lower bounds
for the Hausdorff and lower box counting dimensions of the spectrum can be found
under certain restrictions of the elements of the Fibonacci substitution sequence, and
results from hyperbolic dynamics can be used to show that equality can be achieved
between the two dimensions. |
|
Citation:
|
Dahl, Janine. "The Spectrum of the Off-diagonal
Fibonacci Operator." Doctoral Thesis, Rice University, May, 2010. ETD http://hdl.handle.net/1911/64413. |
|
Citable link to this page:
|
http://hdl.handle.net/1911/64413 |
|
Date:
|
2011 |
