In this talk, I will discuss some results obtained in my Ph.D. thesis.
First, the point mass formula will be introduced. Using the formula, we
shall see how the asymptotics of orthogonal polynomials relate to the
perturbed Verblunsky coefficients. Then I will discuss two classes of
measures on the unit circle -- one with Verblunsky coefficients \alpha_n -->
0 and the other one with \alpha_n --> L (non-zero) -- and explain the
methods I used to tackle the point mass problem involving these measures.
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