Erratum to the article ``Beurling's theorem for nilpotent Lie groups'' Osaka J. Math. 48 (2011), 127--147

Here W is a suitable cross-section for the generic coadjoint orbit s in g , the vector space dual ofg. The condition (1.1) of this theorem depends on the choice of t he bases for which the norm of x in G is defined. We must define the norm of x in G before stating Theorem 1.3. For this we must fix a bases of g, and then define the norm of x using this bases. In addition, we shouldn’t modify this bases t hroughout the proof of Theorem 1.3. This implies that, Remark 2.5.1 in the paper is n ot correct.