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Some Best Constants in the Landau Inequality on a Finite Interval

✍ Scribed by Bengt-Olov Eriksson

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
408 KB
Volume
94
Category
Article
ISSN
0021-9045

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✦ Synopsis

An additive form of the Landau inequality for

is proved for 0<c (cos(?Â2n)) &2 , 1 m n&1, with equality for

, where T n is the Chebyshev polynomial.

From this follows a sharp multiplicative inequality,

For these values of _, the result confirms Karlin's conjecture on the Landau inequality for intermediate derivatives on a finite interval. For the proof of the additive inequality a Duffin and Schaeffer-type inequality for polynomials is shown. 1998 Academic Press n, m (2 n&1 n !) &mÂn T (m) n (1)=M n, m , with equality for n=2 and n=3. In 1970 Article No. AT983203 420

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