From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals

  • Juan C. García-Ardila
  • Francisco MarcellánEmail author
  • Misael E. Marriaga
Conference paper
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)


In this contribution, we present an overview of standard orthogonal polynomials by using an algebraic approach. Discrete Darboux transformations of Jacobi matrices are studied. Next, we emphasize the role of semiclassical orthogonal polynomials as a basic background to analyze sequences of polynomials orthogonal with respect to a Sobolev inner product. Some illustrative examples are discussed. Finally, we summarize some results in multivariate Sobolev orthogonal polynomials.


Orthogonal polynomials Discrete Darboux transformations Semi-classical functionals Sobolev orthogonal polynomials 

Mathematics Subject Classification (2000)

Primary 42C05; Secondary 33C45 33D50 



The authors acknowledge the careful revision of the manuscript by the referees. Their comments and suggestions have contributed to improve its presentation.

The work of J. C. García-Ardila, F. Marcellán and M. Marriaga has been supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía, Industria y Competitividad of España, research project [MTM2015-65888-C4-2-P].


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Authors and Affiliations

  • Juan C. García-Ardila
    • 1
  • Francisco Marcellán
    • 2
    • 3
    Email author
  • Misael E. Marriaga
    • 4
  1. 1.Departamento de Matemática Aplicada a la Ingeniería IndustrialUniversidad Politécnica de MadridMadridSpain
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridLeganésSpain
  3. 3.Instituto de Ciencias Matemáticas (ICMAT)MadridSpain
  4. 4.Departamento de Matemática Aplicada, Ciencia e Ingeniería de Materiales y Tecnología ElectrónicaUniversidad Rey Juan CarlosMóstolesSpain

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