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Operators preserving orthogonality of polynomials

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Marcellán F., Szafraniec F. H.

Studia Mathematica

1996

tom 120

nr 3

205-218

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.

Ograniczanie wyników

1 Studia Mathematica

1 Marcellán F.

1 Szafraniec F. H.

1 1996

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Operators preserving orthogonality of polynomials