We consider functions satisfying the subcritical Beurling's condition, viz.,
for some 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.
© 2015 by De Gruyter