On the convergence of type I Hermite-Pade approximants Articles uri icon

publication date

  • March 2015

start page

  • 124

end page

  • 148

volume

  • 273

international standard serial number (ISSN)

  • 0001-8708

electronic international standard serial number (EISSN)

  • 1090-2082

abstract

  • También publicado en arXiv:1307.0213 Abstract: Fade approximation has two natural extensions to vector rational approximation through the so-called type I and type II Hermite-Pade approximants. The convergence properties of type II Hermite-Pade approximants have been studied. For such approximants Markov and Stieltjes type theorems are available. To the present, such results have not been obtained for type I approximants. In this paper, we provide Markov and Stieltjes type theorems on the convergence of type I Hermite-Pade approximants for Nikishin systems of functions.

keywords

  • multiple orthogonal polynomials; nikishin systems; type i hermite-padé approximants