Divergence of general localized operators on the sets of measure zero

2009/12/08 by G. A. Karagulyan, Karagulyan, G. A.
Mathematics · #42A20 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.CA #msc:42A20

paper · pdf · doi:10.48550/arxiv.0912.1453

6 pages

arxiv created 2009/12/08 · openalex publication_date 2009/12/08 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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∈ E. This result is a generalization of analogous theorems known for the Fourier sums operators with respect to different orthogonal systems.

Related

• On the divergence of Féjer means with respect to Vilenkin systems on the set of measure zero
• On the convergence sets of operator sequences on spaces of homogeneous type
• Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions
• The quantitative isoperimetric inequality for the Hilbert-Schmidt norm of localization operators
• Microlocal properties of Shubin pseudodifferential and localization operators