Geodesic
Operators preserving orthogonality of polynomials
Studia Mathematica, Tome 120 (1996) no. 3, pp. 205-218

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions for polynomials orthogonal on the unit circle.
DOI : 10.4064/sm-120-3-205-218
Keywords: Laguerre polynomials, polynomials orthogonal on the unit circle, linear operators preserving orthogonality

Francisco Marcellán 1 ;  1

1 
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Francisco Marcellán;  . Operators preserving orthogonality of polynomials. Studia Mathematica, Tome 120 (1996) no. 3, pp. 205-218. doi: 10.4064/sm-120-3-205-218

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