Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces

    Authors

    D. H. Kim; S. H. Kim; K. H. Kwon;X. Li

    Comments

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    Abbreviated Journal Title

    Constr. Approx.

    Keywords

    best polynomial approximation; orthogonal polynomials; ORTHOGONAL POLYNOMIALS; Mathematics

    Abstract

    We investigate limiting behavior as gamma tends to infinity of the best polynomial approximations in the Sobolev-Laguerre space W-N,W-2([0, infinity); e(-x)) and the Sobolev-Legendre space W-N,W-2([-1, 1]) with respect to the Sobolev-Laguerre inner-product phi(f,g): = Sigma(k=0)(N-1)a(k) integral(0)(infinity) f((k))(x)g((k))(x)e(-x) dx + gamma integral(0)(infinity) f((N))(x)g((N))(x)e(-x) dx and with respect to the Sobolev-Legendre inner product phi(1)(f,g): = Sigma(k=0)(N-1)a(k) integral(-1)(1) f((k))(x)g((k))(x) dx + gamma integral(-1)(1) f((N))(x)g((N))(x)dx, respectively, where a(0) = 1, a(k) greater than or equal to 0, 1 less than or equal to k less than or equal to N - 1, gamma > 0, and N greater than or equal to 1 is an integer.

    Journal Title

    Constructive Approximation

    Volume

    18

    Issue/Number

    4

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    551

    Last Page

    568

    WOS Identifier

    WOS:000177703400005

    ISSN

    0176-4276

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