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A note on the Geronimus transformation and Sobolev orthogonal polynomials

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Abstract

In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products.

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Author notes

  1. Maxim Derevyagin

    Present address: Department of Mathematics, KU Leuven, Celestijnenlaan 200b, box 2400, 3001, Heverlee, Belgium

Authors and Affiliations

  1. Department of Mathematics MA 4-2, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Maxim Derevyagin

  2. Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain

    Francisco Marcellán

Authors
  1. Maxim Derevyagin
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  2. Francisco Marcellán
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Correspondence to Maxim Derevyagin.

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Derevyagin, M., Marcellán, F. A note on the Geronimus transformation and Sobolev orthogonal polynomials. Numer Algor 67, 271–287 (2014). https://doi.org/10.1007/s11075-013-9788-6

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  • DOI: https://doi.org/10.1007/s11075-013-9788-6

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