Geodesic
A new generator of third-degree linear forms
Problemy analiza, Tome 13 (2024) no. 2, pp. 63-83

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This paper examines linear forms of the third-degree, i.e., when the associated Stieltjes function satisfies a cubic equation with polynomial coefficients. A generator for third-degree forms is constructed. In fact, we study the stability of the third-degree character under this transformation that generalizes the rational spectral transformation. Moreover, we prove the stability of third-degree linear forms under standard algebraic operations. Several illustrative examples are shown.
Keywords: Stieltjes function, third-degree forms
Mots-clés : orthogonal polynomials, rational spectral transformations. 
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     title = {A new generator of third-degree linear forms},
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M. Khalfallah. A new generator of third-degree linear forms. Problemy analiza, Tome 13 (2024) no. 2, pp. 63-83. http://geodesic.mathdoc.fr/item/PA_2024_13_2_a3/