A scheme for interpolation by Hankel translates of a basis function

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Arteaga, Cristian¹  Marrero, Isabel¹ 

[1] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Tenerife, Spain

关键词: Basis function;    Bessel-Kingman hypergroup;    Besse' operator;    Hankel convolution;    Hankel translation;    Minimal norm interpolant;    Sobolev embedding theorem;   

DOI  :  10.1016/j.jat.2012.08.005

来源: Elsevier

【 摘 要 】

This work discusses interpolation of complex-valued functions defined on the positive real axis I by certain special subspaces, in a variational setting that follows the approach of Light and Wayne [W. Light, H. Wayne, Spaces of distributions, interpolation by translates of a basis function and error estimates, Numer. Math. 81 (1999) 415-450]. The set of interpolation points will be a subset {a(1), ... , a(n)} of I and the interpolants will take the form u(x) = Sigma(n)(i=1)alpha(i)(tau(ai)phi)(x) + Sigma(m-1)(j=0) beta(j)p(mu,j)(x) (x is an element of I), where mu >= -1/2, phi is a complex function defined on I (the so-called basis function), p(mu,j) (x) = x(2j+mu+1/2) (j is an element of Z(+), 0 <= j <= m - 1) is a Muntz monomial, tau(z) (z is an element of I) denotes the Hankel translation operator of order mu, and alpha(i), beta(j) (i, j is an element of Z(+), 1 <= i <= n, 0 <= j <= m - 1) are complex coefficients. An estimate for the pointwise error of these interpolants is given. Some numerical examples are included. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free