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(0, 2) Pál-type interpolation on a circle in the complex plane involving Möbius transforms

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Abstract

We study the regularity of certain (0, 2) Pál-type interpolation problems involving the Möbius transforms of the zeros of z 2nρ 2n to the circle ∣z∣ = ρ′.

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References

  1. Kiš, O.: Notes on interpolation. Acta Math. Acad. Sci. Hung. 11, 49–64 (1960) (in Russian)

    Article  Google Scholar 

  2. Pál, L.G.: A new modification of Hermite-Fejér interpolation. Anal. Math 1, 197–205 (1975)

    Article  MathSciNet  Google Scholar 

  3. de Bruin, M.G., Sharma, A., Szabados, J.: Birkhoff type interpolation on petrurbed roots of unity. In memory of: Varma, A.K., Govil, N.K., et al. (eds.) Approximation Theory, pp. 167–179. Marcel Dekker (1998)

  4. de Bruin, M.G., Sharma, A.: Birkhoff interpolation on perturbed roots of unity on the unit circle. J. Nat. Acad. Math. India 11, 83–87 (1997)

    MATH  MathSciNet  Google Scholar 

  5. de Bruin, M.G., Dikshit, H.P., Sharma, A.: Birkhoff interpolation on unity and on Möbius transform of the roots of unity. Numer. Algorithms 23, 115–125 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Brueck, R.: Lagrange interpolation in non-uniformly distributed nodes on the unit circle. Analysis 16, 273–282 (1996)

    MATH  MathSciNet  Google Scholar 

  7. Lorentz, G.G., Riemenschneider, S.D., Jetter, K.: Birkhoff Interpolation. Addison Wisley, MA (1983)

    MATH  Google Scholar 

  8. Bokhari, M.A., Dikshit, H.P., Sharma, A.: Birkhoff interpolation on some perturbed roots of unity: revisisted. Numer. Algorithms 25, 47–62 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dikshit, H.P.: Birkhoff interpolation on some perturbed roots of unity. Nonlinear Anal. Forum 6, 97–102 (2001)

    MATH  MathSciNet  Google Scholar 

  10. de Bruin, M.G.: Regularity of some ‘incomplete’ Pál-type interpolation problems. J. Comput. Appl. Math. 145, 407–415 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. de Bruin, M.G., Dikshit, H.P.: Birkhoff interpolation on nonuniformly distributed points. J. Indian Math. Soc. 69, 81–101 (2002)

    MATH  MathSciNet  Google Scholar 

  12. Dikshit, H.P.: Interpolation on nonuniformly distributed points in the complex plane, In: Dikshit, H.P., Jain, P.K. (eds.) Analysis and Applications, Proceedings of a Conference, pp. 61–91. Narosa Publishing (2002)

  13. Dikshit, H.P.: Pál-type interpolation on nonuniformly distributed nodes on the unit circle. J. Comput. Appl. Math. 155, 253–261 (2003)

    MATH  MathSciNet  Google Scholar 

  14. de Bruin, M.G., Dikshit, H.P.: Pál-type interpolation on nonuniformly distributed points. Numer. Algorithms 40, 1–16 (2005)

    Article  MathSciNet  Google Scholar 

  15. de Bruin, M.G.: (0, m) Pál-type interpolation on the Möbius transform of roots of unity. J. Comput. Appl. Math. 178, 147–153 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. de Bruin, M.G.: (0, m) Pál-type interpolation: interchanging value-and derivative-nodes. J. Comput. Appl. Math. 179, 175–184 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to A. K. Pathak.

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Mandloi, A., Pathak, A.K. (0, 2) Pál-type interpolation on a circle in the complex plane involving Möbius transforms. Numer Algor 47, 181–190 (2008). https://doi.org/10.1007/s11075-008-9165-z

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  • DOI: https://doi.org/10.1007/s11075-008-9165-z

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