ISSN:
1432-0940
Keywords:
41A21
;
31B15
;
Padé approximants
;
Orthogonal polynomials
;
Complex-valued measures
;
Radon-Nikodym derivative
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper we prove the existence of real- and complex-valued measuresμ on the interval [−1,1] with the property that the diagonal Padé approximants [n/n],n=1,2,..., to the functionf(z)=∫dμ(x)/(x−z) neither converge at any fixed pointz∈C∼[−1,1] nor converge in capacity on any open (nonempty) setS inC∼[−1,1]. This result is derived from a theorem on the asymptotic behavior of orthogonal polynomials. It will be shown that it is possible to construct measuresμ. on [−1,1] such that for any arbitrarily prescribed asymptotic behavior there exist subsequences of the associated orthogonal polynomialsQ n that have this behavior.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01890034
Permalink