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Orthogonal Expansion of Real Polynomials, Location of Zeros, and an L2 Inequality

โœ Scribed by G. Schmeisser

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
182 KB
Volume
109
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

Let f (z)=a 0 , 0 (z)+a 1 , 1 (z)+ } } } +a n , n (z) be a polynomial of degree n, given as an orthogonal expansion with real coefficients. We study the location of the zeros of f relative to an interval and in terms of some of the coefficients. Our main theorem generalizes or refines results due to Tura n and Specht. In particular, it includes a best possible criterion for the occurrence of real zeros. Our approach also allows us to establish a weighted L 2 inequality giving a lower estimate for the product of two polynomials.

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