Bezoutians, Euclidean Algorithm, and Orthogonal Polynomials |
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| Authors: | Alain Lascoux Piotr Pragacz |
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| Institution: | (1) CNRS, Institut Gaspard Monge, Université de Marne-la-Vallée, 77454 Marne-la-Vallée, Cedex, France;(2) Center for Combinatorics, LMPC, Nankai University, Tianjin, 300071, P.R. China;(3) Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland |
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| Abstract: | We prove a quadratic expression for the Bezoutian of two univariate polynomials in terms of the remainders for the Euclidean
algorithm. In case of two polynomials of the same degree, or of consecutive degrees, this allows us to interpret their Bezoutian
as the Christoffel- Darboux kernel for a finite family of orthogonal polynomials, arising from the Euclidean algorithm. We
give orthogonality properties of remainders, and reproducing properties of Bezoutians.
Received December 13, 2004 |
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| Keywords: | 05E05 05E35 12D99 15A54 33C47 42C05 |
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