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Some extremal properties of positive trigonometric polynomials

  • V. P. Kondrat'ev
Article

Abstract

For n=8 an upper bound is given for the functional
$$V_n = \mathop {\inf }\limits_{t_n } \frac{{\alpha _1 + \alpha _2 + \cdots + \alpha _n }}{{\left( {\sqrt {\alpha _1 } - \sqrt {\alpha _0 } } \right)^2 }}$$
, which is defined on the class of even, nonnegative, trigonometric polynomials\(t_n (\phi ) = \sum\nolimits_{k = 0}^n {\alpha _k } cos k\phi \), such that α k ⩾ 0 (k=0, ...,n) α10 :Vs ⩽ 34.54461566.

Keywords

Trigonometric Polynomial Extremal Property Positive Trigonometric Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • V. P. Kondrat'ev
    • 1
  1. 1.Institute of Mathematics and Mechanics, Urals Scientific CenterAcademy of Sciences of the USSRUSSR

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