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FULL QUADRATURE SUMS FOR GENERALIZED POLYNOMIALS WITH FREUD WEIGHTS

정해원
대한수학회 (The Korean Mathematical Society)|2010.04|대한수학회논문집 (Communications of the KMS)|제25권 제2호|pp. 215-224

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참고문헌

키워드

generalized polynomialsquadrature sumsFreud weights
주제분류수학

초록

Generalized nonnegative polynomials are defined as products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. In this paper we extend quadrature sums involving pth powers of polynomials to those for generalized polynomials

Abstract

Generalized nonnegative polynomials are defined as products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. In this paper we extend quadrature sums involving pth powers of polynomials to those for generalized polynomials

참고문헌 (16)

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  3. T. Erd´elyi, "Remez-type inequalities on the size of generalized polynomials", J. London Math. Soc., 45(2), pp.255~264 (1992)
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  5. T. Erd´elyi, "Generalized Jacobi weights, Christoffel functions, and zeros of orthogonal polynomials", J. Approx. Theory, 69(2), pp.111~132 (1992)
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  12. D. S. Lubinsky, "Strong Asymptotics for Extremal Polynomials Associated with Weights on R, Lecture Notes in Mathematics, 1305" (1988), Springer-Verlag
  13. D. S. Lubinsky, "Full quadrature sums for pth powers of polynomials with Freud weights", J. Comput. Appl. Math., 60(3), pp.285~296 (1995)
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  16. Y. Xu, "Mean convergence of generalized Jacobi series and interpolating polynomials. II", J. Approx. Theory, 76(1), pp.77~92 (1994)

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