In this paper, we analyze a perturbation of a nontrivial probability measure dμ supported on an infinite subset on the real line, which consists on the addition of a time-dependent mass point. For the associated sequence of monic orthogonal polynomials, we study its dynamics with respect to the time parameter. In particular, we determine the time evolution of their zeros in the special case when the measure is semiclassical. We also study the dynamics of the Verblunsky coefficients, i.e., the recurrence relation coefficients of a polynomial sequence, orthogonal with respect to a nontrivial probability measure supported on the unit circle, induced from dμ through the Szego transformation.
|Title of host publication||Analytic Number Theory, Approximation Theory, and Special Functions|
|Subtitle of host publication||In Honor of Hari M. Srivastava|
|Publisher||Springer New York|
|Number of pages||14|
|ISBN (Print)||1493902571, 9781493902576|
|Publication status||Published - 1 Nov 2014|
|Name||Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava|
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