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Strong Asymptotics for the Continuous Sobolev Orthogonal Polynomials on the Unit Circle |
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| Authors: | A. Aptekarev E. Berriochoa A. Cachafeiro |
| Affiliation: | Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Russiaf2;Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Vigo, Orense, Spain, f3;Departamento de Matemática Aplicada, E.T.S. Ingenieros Industriales, Universidad de Vigo, 36280, Vigo, Spain, f4 |
| Abstract: | Strong (or Szeg-type) asymptotics for orthogonal polynomials with respect to a Sobolev inner product with general measures (the first measure is arbitrary and the second one is absolutely continuous and satisfying a smoothness condition) is obtained. Examples, illustrating the theorems proved, are presented. |
| Keywords: | orthogonal polynomials asymptotic properties Sobolev inner product measures on the unit circle |
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