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Orthogonal polynomials and jump modifications

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1329)

Abstract

Let \(\left\{ {\hat P_n \left( {z,d\alpha } \right)} \right\}\) be a system of orthonormal polynomials on the unit circle U with respect to a measure α and let \(\left\{ {\hat P_n \left( {z,d\beta } \right)} \right\}\) be a system of orthonormal polynomials on U with respect to β (β=α+εδ(t), where t≠U, ε>0, and δ(t) the unit measure supported at z=t). If (en (α))−1/2 and (en (β))−1/2 are their leading coefficients, in this paper we present some properties of the difference en (β)-en(α) and we show that both se quences en (α) and en (β) have the same limit by using the recurrence re lation.

Keywords

  • Unit Circle
  • Orthogonal Polynomial
  • Approximation Theory
  • Unit Measure
  • Consultant Bureau

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References

  1. CACHAFEIRO, M.A.; MARCELLAN, F. "Polinomios ortogonales y medidas singulares sobre curvas". Comunicación a las XI Jornadas Hispano-Lusas de Matemáticas. Badajoz, 1986.

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© 1988 Springer-Verlag

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Cachafeiro, M.A., Marcellán, F. (1988). Orthogonal polynomials and jump modifications. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083362

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  • DOI: https://doi.org/10.1007/BFb0083362

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19489-7

  • Online ISBN: 978-3-540-39295-8

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