Behavior of Shannon's sampling series for hardy spaces

Holger Boche, Ullrich J. Mönich

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper the convergence behavior of the Shannon sampling series is analyzed for Hardy spaces. It is well known that the Shannon sampling series is locally uniformly convergent. However, for practical applications the global uniform convergence is important. It is shown that there are functions in the Hardy space such that the Shannon sampling series is not uniformly convergent on the whole real axis. In fact, there exists a function in this space such that the peak value of the Shannon sampling series diverges unboundedly. The proof uses Fefferman's theorem, which states that the dual space of the Hardy space is the space of functions of bounded mean oscillation.

Original languageEnglish
Pages (from-to)404-412
Number of pages9
JournalJournal of Fourier Analysis and Applications
Volume15
Issue number3
DOIs
StatePublished - Jun 2009
Externally publishedYes

Keywords

  • Hardy space
  • Shannon sampling series
  • Stable reconstruction
  • Uniform convergence

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