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• W2012014452 abstract "The exceptional X1-Jacobi differential expression is a second-order ordinary differential expression with rational coefficients; it was discovered by Gómez-Ullate, Kamran and Milson in 2009. In their work, they showed that there is a sequence of polynomial eigenfunctions {Pˆn(α,β)}n=1∞ called the exceptional X1-Jacobi polynomials. There is no exceptional X1-Jacobi polynomial of degree zero. These polynomials form a complete orthogonal set in the weighted Hilbert space L2((−1,1);wˆα,β), where wˆα,β is a positive rational weight function related to the classical Jacobi weight. Among other conditions placed on the parameters α and β, it is required that α,β>0. In this paper, we develop the spectral theory of this expression in L2((−1,1);wˆα,β). We also consider the spectral analysis of the ‘extreme’ non-exceptional case, namely when α=0. In this case, the polynomial solutions are the non-classical Jacobi polynomials {Pn(−2,β)}n=2∞. We study the corresponding Jacobi differential expression in several Hilbert spaces, including their natural L2 setting and a certain Sobolev space S where the full sequence {Pn(−2,β)}n=0∞ is studied and a careful spectral analysis of the Jacobi expression is carried out." @default.
• W2012014452 created "2016-06-24" @default.
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• W2012014452 date "2015-02-01" @default.
• W2012014452 modified "2023-10-05" @default.
• W2012014452 title "A spectral study of the second-order exceptional <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msub><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-Jacobi differential expression and a related non-classical Jacobi differential expression" @default.
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• W2012014452 doi "https://doi.org/10.1016/j.jmaa.2014.08.016" @default.
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