Two-Orthogonal Polynomial Sequences as Eigenfunctions of a Third-Order Differential Operator

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• 作者：T. Augusta Mesquita ; P. Maroni
• 关键词：d ; orthogonal polynomials ; Appell sequences ; lowering operators ; linear functionals
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：13
• 期：2
• 页码：687-701
• 全文大小：554 KB
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• 作者单位：T. Augusta Mesquita (1) (2)
  P. Maroni (3) (4)
  
  1. Instituto Politécnico de Viana do Castelo, Av. do Atlântico, 4900-348, Viana do Castelo, Portugal
  2. Centro de Matemática da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal
  3. Laboratoire Jacques-Louis Lions, CNRS, UMR 7598, 75005, Paris, France
  4. Laboratoire Jacques-Louis Lions, UPMC Université Paris 06, UMR 7598, 75005, Paris, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

This paper presents functional identities fulfilled by the forms of the dual sequence of polynomial eigenfunctions of certain differential operators, belonging to the class of the two-orthogonal polynomial sequences. For a specific third-order lowering operator, the correspondent matrix differential identity is deduced, proving that the resultant polynomial sequence is a classical polynomial sequence in the Hahn’s sense. As an example, the vectorial relation fulfilled by the tuple of functionals (u ₀, u ₁) of a two-orthogonal polynomial sequences analogous to the classical Laguerre polynomials is given, treated in a work of Ben Cheikh and Douak.