☆ 4.6 Article

Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations

NUMERICAL ALGORITHMS (2023)

Associated orthogonal polynomials of the first kind and Darboux transformations

J. C. Garcia-Ardila et al.

Summary: This article explores quasi-definite linear functionals defined on polynomial spaces and the associated orthogonal polynomial sequences. It analyzes the relations between linear functionals under different transformations. By using LU and UL factorizations, close relations between their corresponding Jacobi matrices are obtained.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2022)

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Article Mathematics, Applied

Symmetric differential operators for Sobolev orthogonal polynomials of Laguerre- and Jacobi-type

Clemens Markett

Summary: This paper discusses Laguerre-Sobolev polynomials on the positive half-line and Jacobi-Sobolev polynomials on the interval [-1, 1], establishing their special relationships with eigenfunctions. New representations of the differential operators for these polynomial systems are presented, reflecting the influence of parameters and demonstrating symmetry with respect to Sobolev inner products to recover orthogonality.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS (2021)

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Article Mathematics