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Divergence of general operators on sets of measure zero

G. A. Karagulyan (2010)

Colloquium Mathematicae

We consider sequences of linear operators Uₙ with a localization property. It is proved that for any set E of measure zero there exists a set G for which U G ( x ) diverges at each point x ∈ E. This result is a generalization of analogous theorems known for the Fourier sum operators with respect to different orthogonal systems.

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