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Orthogonality Preserving Maps and the Laguerre Functional

William R. Allaway
Proceedings of the American Mathematical Society
Vol. 100, No. 1 (May, 1987), pp. 82-86
DOI: 10.2307/2046123
Stable URL: http://www.jstor.org/stable/2046123
Page Count: 5
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Orthogonality Preserving Maps and the Laguerre Functional
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Abstract

Let R[ x ] be the usual algebra of all polynomials in the indeterminate x over the field of real numbers R, and let φ be a linear operator mapping R[ x ] into R[ x ]. In this paper we show that if φ maps every orthogonal polynomial sequence into an orthogonal polynomial sequence, then φ is defined by φ(xn) = s(ax + b)n, n = 0, 1, 2,..., where s, a, and b belong to R, s ≠ 0, and a ≠ 0.

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