Abstract
We study the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product on the unit circle〈f, g〉=∫f(eiθ)g(eiθ)dμ(θ)+f(Z)Ag(Z)H, where f(Z)=(f(z1), …, f(l1)(z1), …, f(zm), …, f(lm)(zm)), A is a M×M positive definite matrix or a positive semidefinite diagonal block matrix, M=l1+…+lm+m, dμ belongs to a certain class of measures, and |zi|>1, i=1, 2, …, m.
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