Operators preserving orthogonality of polynomials

Tom 120 / 1996

Francisco Marcellán, Studia Mathematica 120 (1996), 205-218 DOI: 10.4064/sm-120-3-205-218


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.


  • Francisco Marcellán

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