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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2046123
Page Count: 5
You can always find the topics here!Topics: Polynomials, Real numbers, Mathematical sequences, Orthogonality, Mathematical theorems, Linear transformations, Integers, Algebra
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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.
Proceedings of the American Mathematical Society © 1987 American Mathematical Society