English

Divergence of general localized operators on the sets of measure zero

Classical Analysis and ODEs 2009-12-09 v1

Abstract

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

Keywords

Cite

@article{arxiv.0912.1453,
  title  = {Divergence of general localized operators on the sets of measure zero},
  author = {G. A. Karagulyan},
  journal= {arXiv preprint arXiv:0912.1453},
  year   = {2009}
}

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6 pages