A geometric approach to calculating the limit set of eigenvalues for banded Toeplitz matrices
This thesis is about the limiting eigenvalue distribution of n × n Toeplitz matrices as n → ∞. The two classical questions we want to answer are: what is the limit set of the eigenvalues, and what is the limiting distribution of the eigenvalues. Our main result is a new approach to calculate the limit set Λ(b) for a Laurent polynomial b, i.e. for banded Toeplitz matrices. The approach is geometric