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On the uniform convergence of weighted trigonometric series

Bogdan Szal (2011)

Banach Center Publications

In the present paper we consider a new class of sequences called GM(β,r), which is the generalization of a class defined by Tikhonov in [15]. We obtain sufficient and necessary conditions for uniform convergence of weighted trigonometric series with (β,r)-general monotone coefficients.

On two-scale convergence and related sequential compactness topics

Anders Holmbom, Jeanette Silfver, Nils Svanstedt, Niklas Wellander (2006)

Applications of Mathematics

A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L 2 ( Ω ) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.

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