Asymptotic behaviour of Sobolev orthogonal polynomials on the unit circle

作者：Castillo Kenier^*; Garza Luis E; Marcellan Francisco

来源：Integral Transforms and Special Functions, 2013, 24(1): 23-38.

DOI：10.1080/10652469.2011.649751

• probability measures on the unit circle
• orthogonal polynomials
• Sobolev inner products
• outer relative asymptotics
• zeros
• 42C05
• 33C47

In this contribution, we deal with analytic properties of sequences of polynomials orthogonal with respect to a Sobolev-type inner product %26lt;br%26gt;where mu is a non-trivial probability measure supported on the unit circle. We focus our attention on the outer relative asymptotics of these polynomials in terms of those associated with the measure mu. The behaviour of their zeros in terms of the parameter ? is studied in some illustrative examples.

• 出版日期2013-1-1