Direct form seminorms arising in the theory of interpolation by Hankel translates of a basis function

  • Authors:

  • Cristian Arteaga;Isabel Marrero

  • Affiliations:

  • Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Spain 38271;Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Spain 38271

  • Venue:
  • Advances in Computational Mathematics
  • Year:
  • 2014

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Abstract

Certain spaces of functions which arise in the process of interpolation by Hankel translates of a basis function, as developed by the authors elsewhere, are defined with respect to a seminorm which is given in terms of the Hankel transform of each function. This kind of seminorm is called an indirect one. Here we discuss essentially two cases in which the seminorm can be rewritten in direct form, that is, in terms of the function itself rather than its Hankel transform. This is expected to lead to better estimates of the interpolation error.