ArticleOriginal scientific text
Title
Operators preserving orthogonality of polynomials
Authors 1, 2
Affiliations
- Escuela Politécnica Superior, Universidad Carlos III de Madrid, E-28911 Leganés, c/Butarque, 15, Spain
- Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30059 Kraków, Poland
Abstract
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.
Keywords
Laguerre polynomials, polynomials orthogonal on the unit circle, linear operators preserving orthogonality
Bibliography
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Pages:
205-218
Main language of publication
English
Received
1995-01-20
Accepted
1996-04-17
Published
1996
Exact and natural sciences