Journal of the Australian Mathematical Society

Research Article

VARIANTS OF MIYACHI’S THEOREM FOR NILPOTENT LIE GROUPS

ALI BAKLOUTIa1 and SUNDARAM THANGAVELUa2 c1

a1 Department of Mathematics, Faculty of Sciences at Sfax, Route de Soukra, 3038, Sfax, Tunisia (email: Ali.Baklouti@fss.rnu.tn)

a2 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India (email: veluma@math.iisc.ernet.in)

Abstract

We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

(Received February 27 2009)

(Accepted August 30 2009)

2000 Mathematics subject classification

  • primary 22E25; secondary 22G15

Keywords and phrases

  • uncertainty principles;
  • Plancherel formula;
  • nilpotent Lie group

Correspondence:

c1 For correspondence; e-mail: veluma@math.iisc.ernet.in

Footnotes

The first author was supported by D.G.R.S.R.T., Research Unity 00 UR 1501 and the second author by a J.C. Bose Fellowship from DST.