Determining Singularities Using Row Sequences of Padé-orthogonal Approximants Articles uri icon

publication date

  • December 2013

start page

  • 179

end page

  • 208

issue

  • 2

volume

  • 5

international standard serial number (ISSN)

  • 1889-3066

electronic international standard serial number (EISSN)

  • 1989-7251

abstract

  • Starting from the orthogonal polynomial expansion of a function F corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Pad\'{e}-orthogonal approximants). We obtain both direct and inverse results relating the convergence of the poles of the approximants and the singularities of F. Thereby, we obtain analogues of the theorems of E. Fabry, R. de Montessus de Ballore, V.I. Buslaev, and S.P. Suetin.

keywords

  • padé approximants ; orthogonal polynomials ; fabry’s theorem ; montessus de ballore’s theorem