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On Certain Duffin and Schaeffer Type Inequalities

✍ Scribed by Geno Nikolov

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
285 KB
Volume
93
Category
Article
ISSN
0021-9045

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✦ Synopsis

Duffin and Schaeffer type inequalities related to some ultraspherical polynomials are established. One of the results obtained reads as follows: Let f be a real algebraic polynomial of degree at most n,

  1. for all k # [1, ..., n]. Moreover, equality holds if and only if f =\T n . 1998 Academic Press for k=1, ..., n. Equality holds only for f (x)=\T n (x)=\cos(n arccos x). Inequalities of the brothers Markov type have been a challenge for many mathematicians. In 1941 Duffin and Schaeffer [4] strengthened Theorem A Article No. AT973140 157

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