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L p-convergence of Lagrange interpolation on the semiaxis

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Abstract

In order to approximate functions defined on (0, +∞), the authors consider suitable Lagrange polynomials and show their convergence in weighted L p-spaces.

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References

  1. R. Askey and S. Wainger, Mean convergence of expansion in Laguerre and Hermite series, Amer. J. Math., 87 (1965), 695–708.

    Article  MATH  MathSciNet  Google Scholar 

  2. Z. Ditzian and V. Totik, Moduli of Smoothness, SCMG Springer-Verlag, (New York, 1987).

    MATH  Google Scholar 

  3. K. G. Ivanov, On the behaviour of two moduli of functions, II Serdica, 12, 196–203.

  4. T. Kasuga and R. Sakai, Orthonormal polynomials with generalized Freud-type weights, J. Approx. Theory, 121 (2003), 13–53.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. L. Levin and D. S. Lubinski, Christoffel functions, orthogonal polynomials and Nevai’s conjecture for Freud weights, Constr. Approx., 8 (1992), 463–535.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. L. Levin and D. S., Lubinski, Orthogonal polynomials for weights x 2ρ e −2Q(x) on [0, d), J. Approx. Theory, 134 (2005), 199–256.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. Mastroianni and G. V. Milovanović, Some numerical methods for second kind Fredholm integral equation on the real semiaxis, to appear.

  8. G. Mastroianni and G. V. Milovanović, Interpolation Processes: Basic Theory and Applications, in progress.

  9. G. Mastroianni and J. Szabados, Polynomial approximation on infinite intervals with weights having inner zeros, Acta Math. Hungar., 96 (2002), 221–258.

    Article  MATH  MathSciNet  Google Scholar 

  10. G. Mastroianni and J. Szabados, Direct and converse polynomial approximation theorems on the real line withh weights having zeros, in: Frontiers in Interpolation and Approximation, Dedicated to the memory of A. Sharma, eds. N. K. Govil, H. N. Mhaskar, R. N. Mohapatra, Z. Nashed and J. Szabados, Taylor & Francis Books, Boca Raton, Florida (2006), pp. 287–306.

    Google Scholar 

  11. G. Mastroianni and J. Szabados, Polynomial approximation on the real semiaxis with generalized Laguerre weights, Studia Univ. Babeş-Bolyai, Mathematica, 52 (2007), 105–128.

    Google Scholar 

  12. G. Mastroianni and P. Vértesi, Fourier sums and Lagrange interpolation on (0, +∞) and (−∞, +∞), in: Frontiers in Interpolation and Approximation, Dedicated to the memory of A. Sharma, eds. N. K. Govil, H. N. Mhaskar, R. N. Mohapatra, Z. Nashed and J. Szabados, Taylor & Francis Books, Boca Raton, Florida (2006), pp. 307–344.

    Google Scholar 

  13. H. N. Mhaskar, Introduction to the Theory of Weighted Polynomial Approximation, World Scientific (Singapore, New Jersey, London, Hong Kong, 1996).

    MATH  Google Scholar 

  14. B. Muckenhoupt, Mean convergence of Hermite and Laguerre series II, Trans. Amer. Math. Soc., 147 (1970), 433–460.

    Article  MathSciNet  Google Scholar 

  15. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer (Berlin, 1997).

    MATH  Google Scholar 

  16. P. Vértesi, Oral communication.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università della Basilicata, Via dell’Ateneo Lucano 10, 85100, Potenza, Italy

    C. Laurita & G. Mastroianni

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  1. C. Laurita
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  2. G. Mastroianni
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Correspondence to C. Laurita.

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Laurita, C., Mastroianni, G. L p-convergence of Lagrange interpolation on the semiaxis. Acta Math Hung 120, 249–273 (2008). https://doi.org/10.1007/s10474-008-7119-5

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  • DOI: https://doi.org/10.1007/s10474-008-7119-5

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