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Displaying similar documents to “Some new inequalities for trigonometric polynomials with special coefficients.”

On the behavior near the origin of double sine series with monotone coefficients

Xhevat Z. Krasniqi (2009)

Mathematica Bohemica

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In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients a k , l satisfy certain conditions) the following order equality is proved g ( x , y ) ∼ m n a m , n + m n ∑ l = 1 n - 1 l a m , l + n m ∑ k = 1 m - 1 k a k , n + 1 m n ∑ l = 1 n - 1 ∑ k = 1 m - 1 k l a k , l , where x ∈ ( π m + 1 , π m ] , y ∈ ( π n + 1 , π n ] , m , n = 1 , 2 , ⋯ .

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) ≤ λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ₂ ( 2 ) ) ≥ λ ( V ) for any two-dimensional real symmetric space V.