The differential equation for Jacobi–Sobolev orthogonal polynomials with two linear perturbutions

Markett, Clemens

doi:10.1016/j.jat.2022.105782

Journal of Approximation Theory

2022

DOI: 10.1016/j.jat.2022.105782

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The differential equation for Jacobi–Sobolev orthogonal polynomials with two linear perturbutions

Clemens Markett

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Cited by 5 publications

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Recovering orthogonality from quasi‐type kernel polynomials using specific spectral transformations

Kumar,

Swaminathan

2024

Math Methods in App Sciences

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In this work, the concept of quasi‐type Kernel polynomials with respect to a moment functional is introduced. Difference equation satisfied by these polynomials along with the criterion for orthogonality conditions are discussed. The process of recovering orthogonality for the linear combination of a quasi‐type kernel polynomial with another orthogonal polynomial, which is identified by involving linear spectral transformation, is provided. This process involves an expression of ratio of iterated kernel polynomials. This leads to considering the limiting case of ratio of kernel polynomials involving continued fractions. Special cases of such ratios in terms of certain continued fractions are exhibited. Moreover, examples are discussed for obtaining the orthogonality of quasi‐type kernel polynomials of order 1.

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Recovering orthogonality from quasi‐type kernel polynomials using specific spectral transformations

Kumar,

Swaminathan

2024

Math Methods in App Sciences

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Bispectrality for matrix Laguerre-Sobolev polynomials

Marcellán,

Zurrián

2024

Linear Algebra and its Applications

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On convergence of Fourier series in discrete Jacobi–Sobolev spaces

Ciaurri

Ceniceros

Rodríguez

2023

Integral Transforms and Special Functions

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The differential equation for Jacobi–Sobolev orthogonal polynomials with two linear perturbutions

Cited by 5 publications

References 20 publications

Recovering orthogonality from quasi‐type kernel polynomials using specific spectral transformations

Recovering orthogonality from quasi‐type kernel polynomials using specific spectral transformations

Bispectrality for matrix Laguerre-Sobolev polynomials

On convergence of Fourier series in discrete Jacobi–Sobolev spaces

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