About measures and nodal systems for which the Hermite interpolants uniformly converge to continuous functions on the circle and interval |
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Authors: | E. Berriochoa,E. Martí nez |
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Affiliation: | a Departamento de Matemática Aplicada I, Facultad de Ciencias, Universidad de Vigo, Ourense, Spain b Departamento de Matemática Aplicada I, Escuela de Ingeniería Industrial, Universidad de Vigo, 36310 Vigo, Spain |
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Abstract: | We obtain the Laurent polynomial of Hermite interpolation on the unit circle for nodal systems more general than those formed by the n-roots of complex numbers with modulus one. Under suitable assumptions for the nodal system, that is, when it is constituted by the zeros of para-orthogonal polynomials with respect to appropriate measures or when it satisfies certain properties, we prove the convergence of the polynomial of Hermite-Fejér interpolation for continuous functions. Moreover, we also study the general Hermite interpolation problem on the unit circle and we obtain a sufficient condition on the interpolation conditions for the derivatives, in order to have uniform convergence for continuous functions.Finally, we obtain some improvements on the Hermite interpolation problems on the interval and for the Hermite trigonometric interpolation. |
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Keywords: | Hermite interpolation Hermite-Fejé r interpolation Laurent polynomials Convergence Unit circle Orthogonal polynomials Para-orthogonal polynomials Szeg? class |
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