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Infinite finite range inequalities

정해원
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2010.03|한국수학논문집 (Korean Journal of Mathematics)|제18권 제1호|pp. 63-77

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키워드

generalized polynomialsinfinite finite range inequalitiesweighted polynomials
주제분류수학

초록

Infinite finite range inequalities relate the norm of a weighted polynomial over R to its norm over a finite interval. In this paper we extend such inequalities to generalized polynomials with the weight W(x)=∏k=1m |x-xk|□k · exp(-|x|α).

Abstract

Infinite finite range inequalities relate the norm of a weighted polynomial over R to its norm over a finite interval. In this paper we extend such inequalities to generalized polynomials with the weight W(x)=∏k=1m |x-xk|□k · exp(-|x|α).

참고문헌 (12)

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  3. T. Erdelyi, "Inequalities for generalized nonnegative poly-nomials", Constr. Approx., 8, pp.241~255 (1992)
  4. T. Erdelyi, "Generalized Jacobi weights, Christoffel functions and zeros of orthogonal polynomials", J. Approx. Theory, 69, pp.111~132 (1992)
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  6. A.L. Levin, "Canonical products and the weights exp(-ΙxΙα), α > 1, with applications", J. Approx. Theory, 49, pp.149~169 (1987)
  7. D.S. Lubinsky, "A proof of Freud's conjecture for exponential weights", Constr. Approx., 4, pp.65~83 (1988)
  8. H.N. Mhaskar, "Extremal problems for polynomials with exponential weights", Trans. Amer. Math. Soc., 285, pp.203~234 (1984)
  9. H.N. Mhaskar, "Where does the Sup Norm of a Weighted Polyno-mial Live?", Constr. Approx., 1, pp.71~91 (1985)
  10. P. Nevai, "Bernstein's inequality in Lp for 0 < p < 1", J. Approx. Theory., 27, pp.239~243 (1979)
  11. P. Nevai, "Orthogonal Polynomials and Christoffel Functions. A Case Study", J. Approx. Theory., 48, pp.3~167 (1986)
  12. P. Nevai, "Orthogonal polynomials", Mem. Amer. Math. Soc., 213 (1979)

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