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-Coherent Pairs on the Unit Circle

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  • Luis Garza
  • Francisco Marcellán
  • Natalia C. Pinzón-Cortés

Abstract

A pair of Hermitian regular linear functionals on the unit circle is said to be a -coherent pair if their corresponding sequences of monic orthogonal polynomials and satisfy , , , where . In this contribution, we consider the cases when is the linear functional associated with the Lebesgue and Bernstein-Szegő measures, respectively, and we obtain a classification of the situations where is associated with either a positive nontrivial measure or its rational spectral transformation.

Suggested Citation

  • Luis Garza & Francisco Marcellán & Natalia C. Pinzón-Cortés, 2013. "-Coherent Pairs on the Unit Circle," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, November.
  • Handle: RePEc:hin:jnlaaa:307974
    DOI: 10.1155/2013/307974
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