Equiconvergence for perturbed Jacobi polynomial expansions

We show asymptotic expansions of the eigenfunctions of certain perturbations of the Jacobi operator in a bounded interval, deducing equiconvergence results between expansions with respect to the associated orthonormal basis and expansions with respect to the cosine basis. Several results for pointwi...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-09, Vol.525 (2), p.127147, Article 127147
Main Authors: Gigante, Giacomo, Jotsaroop, K.
Format: Article
Language:English
Subjects:
Equiconvergence
Jacobi polynomial expansions
Sturm-Liouville operators
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Summary:We show asymptotic expansions of the eigenfunctions of certain perturbations of the Jacobi operator in a bounded interval, deducing equiconvergence results between expansions with respect to the associated orthonormal basis and expansions with respect to the cosine basis. Several results for pointwise convergence then follow.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127147