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On the Lebesgue function of weighted Lagrange interpolation. II

  • P. Vértesi (a1)

Abstract

The aim of this paper is to continue our investigation of the Lebesgue function of weighted Lagrange interpolation by considering Erdős weights on ℝ and weights on [−1, 1]. The main results give lower bounds for the Lebesgue function on large subsets of the relevant domains.

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References

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[1]Damelin, S., ‘The Lebesgue function and Lebesgue constant of Lagrange interpolation for Erdős weights’, J. Approx. Theory (to appear).
[2]Damelin, S., ‘Lebesgue bounds for exponential weights on [−1, 1]’, Acta Math. Hungar. (to appear).
[3]Erdős, P. and Turán, P., ‘On interpolation III’, Ann. of Math. 41 (1940), 510553.
[4]Levin, A. L. and Lubinsky, D. S., Christoffel functions and orthogonal polynomials for exponential weights on [−1, 1], Mem. Amer. Math. Soc. 535, Vol. 111 (1994).
[5]Levin, A. L. and Lubinsky, D. S. and Mtembu, T. Z., ‘Christoffel functions and orthogonal polynomials for Erdós weights on (−∞, ∞)’, Rend. Mat. Appl. (7) 14 (1994), 199289.
[6]Lubinsky, D. S., ‘Lx Markov and Bernstein inequalities for Erdós weights’, J. Approx. Theory 60 (1990), 188230.
[7]Lubinsky, D. S., ‘An extension of the Erdós-Turán inequality for the sum of successive fundamental polynomials’, Ann. of Numer. Math. 2 (1995), 305309.
[8]Mastroianni, G. and Russo, M. G., ‘Weighted Lagrange interpolation for Jacobi weights’, Technical Report.
[9]Mastroianni, G. and Totik, V.; ‘Weighted polynomial inequalities with doubling and Ax weights’, J. Approx. Theory (to appear).
[10]Mastroianni, G. and Vértesi, P., ‘Some applications of generalized Jacobi weights’, Acta Math. Hungar. 77, (1997), 323357.
[11]Szabados, J., ‘Weighted Lagrange interpolation polynomials’, J. Inequal. Appl. 1 (1997), 99123.
[12]Szabados, J., ‘Weighted Lagrange and Hermite-Fejér interpolation on the real line’, Technical Report.
[13]Szabados, J. and Vértesi, P., Interpolation of functions (World Scientific, Singapore, New Jersey, London, Hong Kong, 1990).
[14]PVértesi, , ‘New estimation for the Lebesgue function of Lagrange interpolation’, Acta Math. Acad. Sci. Hungar. 40 (1982), 2127.
[15]Vértesi, P., ‘On the Lebesgue function of weighted Lagrange interpolation. I’, Constr. Approx. (to appear).
[16]Vértesi, P., ‘Weighted Lagrange interpolation for generalized Jacobi weights’, Technical Report (to appear).
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On the Lebesgue function of weighted Lagrange interpolation. II

  • P. Vértesi (a1)

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