Divergence of general localized operators on the sets of measure zero

Details Divergence of general localized operators on the sets of measure zero Divergence of general localized operators on the sets of measure zero

2009-12-08

arxiv.org/abs/0912.1453v1

Mathematics

Classical Analysis and ODEs

6 pages

Scientific paper

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

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