Interaction between the Fourier transform and the Hilbert transform

  • Elijah Liflyand Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900
Keywords: Fourier transform, Hilbert transform, real Hardy space, atomic decomposition, Hardy's inequality, bounded variation

Abstract

Well-known and recently observed situations where the two main transforms in harmonic analysis, the Fourier transform and the Hilbert transform, show their adjacency and interplay in a specic interesting manner are overviewed. Some relations of that kind are new, while in other cases well-known formulas are considered in a different setting.

Downloads

Download data is not yet available.
Published
2014-06-25
Section
Articles