• Senior Thesis
• Department of Mathematics
• Harvey Mudd College

Dave Gaebler

Harvey Mudd College Mathematics 2004

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.