Dave Gaebler

Harvey Mudd College Mathematics 2004

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Thesis Proposal: Toeplitz Operators on Locally Compact Abelian Groups
Thesis Advisor: Prof. Henry A. Krieger
Second Reader: Prof. Michael R. Raugh
E-Mail: dgaebler@hmc.edu
Final Draft: Asymptotic Eigenvalue Distributions of Toeplitz Operators

Toeplitz Operators on Locally Compact Abelian Groups

I will be studying the asymptotic eigenvalue distributions of self-adjoint finite Toeplitz operators on locally compact Abelian groups. In the special case of the circle group, it is known that the eigenvalue distribution depends on the Radon-Nikodym derivative of the absolutely continuous part of the measure. However, it is not known whether this result generalizes to other locally compact Abelian groups; in particular, it is not known whether the singular part of the measure has any effect on the asymptotic eigenvalue distribution.