Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on the Unit Circle |
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| Authors: | Ana Foulqui Moreno, Francisco Marcell n,K. Pan |
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| Affiliation: | Departamento de Matemática, Universidade de Aveiro, Campus de Santiago, 3810, Aveiro, Portugalf1;Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, C. Butarque 15, 28911, Leganés-Madrid, Spain, f2;Department of Mathematics and Computer Science, Barry University, Miami shores, Florida, 33161, U.S.A., f3 |
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| Abstract: | We study the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product on the unit circle 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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