Strong Asymptotic Behavior and Weak Convergence of Polynomials Orthogonal on an Arc of the Unit Circle.

  1. Hernández, M.B. 1
  2. Díaz, E.M. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Inst. Sup. Cie. y Tecnologias Nucl., Ave. Salvador Allende y Luaces, 10600, Habana, Cuba
Revista:
Journal of Approximation Theory

ISSN: 0021-9045

Any de publicació: 2001

Volum: 111

Número: 2

Pàgines: 233-255

Tipus: Article

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DOI: 10.1006/JATH.2001.3574 SCOPUS: 2-s2.0-0005862409 WoS: WOS:000170502200005 GOOGLE SCHOLAR

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Resum

Let σ be a finite positive Borel measure supported on an arc γ of the unit circle, such that σ′>0 a.e. on γ. We obtain a theorem about the weak convergence of the corresponding sequence of orthonormal polynomials. Moreover, we prove an analogue of the Szego-Geronimus theorem on strong asymptotics of the orthogonal polynomials on the complement of γ, which completes to its full extent a result of N. I. Akhiezer. The key tool in the proofs is the use of orthogonality with respect to varying measures. © 2001 Academic Press.