• Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/105/02/0135-0151

    • Keywords

       

      Fourier transform; Heisenberg group; motion group; uncertainty principle

    • Abstract

       

      There are several ways of formulating the uncertainty principle for the Fourier transform on ℝn. Roughly speaking, the uncertainty principle says that if a functionf is ‘concentrated’ then its Fourier transform$$\tilde f$$ cannot be ‘concentrated’ unlessf is identically zero. Of course, in the above, we should be precise about what we mean by ‘concentration’. There are several ways of measuring ‘concentration’ and depending on the definition we get a host of uncertainty principles. As several authors have shown, some of these uncertainty principles seem to be a general feature of harmonic analysis on connected locally compact groups. In this paper, we show how various uncertainty principles take form in the case of some locally compact groups including ℝn, the Heisenberg group, the reduced Heisenberg groups and the Euclidean motion group of the plane.

    • Author Affiliations

       

      A Sitaram1 M Sundari1 S Thangavelu1

      1. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore - 560 059, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.