Displaying similar documents to “Integrability of cosine trigonometric series with coefficients of bounded variation.”

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 , ⋯ .

An Ingham type proof for a two-grid observability theorem

Michel Mehrenberger, Paola Loreti (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1 D -wave equation for a time T > 2 2 ; this time, if the observation is made in ( - T / 2 , T / 2 ) , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.