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Accessible Unlicensed Requires Authentication Published by De Gruyter June 4, 2015

Variations on a theorem of Beurling

Rahul Garg and Sundaram Thangavelu

Abstract

We consider functions satisfying the subcritical Beurling's condition, viz.,

nn|f(x)||f^(y)|ea|x·y|dxdy<

for some 0<a<1. We show that such functions are entire vectors for the Schrödinger representations of the Heisenberg group. If an eigenfunction f of the Fourier transform satisfies the above condition, we show that the Hermite coefficients of f have certain exponential decay which depends on a.

We wish to thank the referee for carefully reading the manuscript and making useful suggestions which have been followed in this revised version.

Received: 2014-11-29
Accepted: 2015-5-7
Published Online: 2015-6-4
Published in Print: 2015-7-1

© 2015 by De Gruyter