On the Minimum of the Wehrl Entropy for a Locally Compact Abelian Group

A construction of the Wehrl entropy is proposed for an arbitrary locally compact abelian group \(G\) . It is proved that the Wehrl entropy is not less than a certain nonnegative integer, which is an invariant of the group \(G\) . The minimum of the Wehrl entropy is attained on coherent states.