Zero location and n-th root asymptotics of Sobolev orthogonal polynomials

López Lagomasino, Guillermo; Pijeira, Héctor

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Zero location and n-th root asymptotics of Sobolev orthogonal polynomials

Author(s): López Lagomasino, Guillermo; Pijeira, Héctor

Publisher: Elsevier

Issued date: 1999-07

Citation: Journal of Approximation Theory, 1999, vol. 99, n. 1, p. 30-43

ISSN: 0021-9045

DOI: 10.1006/jath.1998.3318

Sponsor: Research by the first author (G.L.L.) was partially supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01 and by INTAS under Grant 93-0219 EXT. Research by the second author (H.P.) carried out while following a Doctoral Program at Universidad Carlos III de Madrid under grant from Agencia Española de Cooperación Internacional.

Review: PeerReviewed

Publisher version: http://dx.doi.org/10.1006/jath.1998.3318

Keywords: Sobolev orthogonal polynomials , Borel measures , Zeros , Dirac measure

URI: http://hdl.handle.net/10016/6363

Rights: © Elsevier

Abstract:

For a wide class of Sobolev orthogonal polynomials, it is proved that their zeros are contained in a compact subset of the complex plane and the asymptotic zero distribution is obtained. With this information, the nth root asymptotic behavior outside the compa [+]