GEVREY SPACES AND THEIR INTERSECTIONS

For unbounded operators A1,...,A(d), Gevrey spaces S(lambda1,...,lambda(d))(A1,...,A(d)) of order (lambda1,...,lambda(d)) are introduced, where the orders lambda1,...,lambda(d) need not be equal. These extend the notion of Gevrey space defined by Goodman and Wallach where lambda1=...=lambda(d). Several mild conditions on the operators A1,...,A(d) and the orders lambda1,...,lambda(d) are presented such that the equality S(lambda1,...,lambdad)(A1,...,A(d)) = and(k=1)d S(lambdak)(A(k)) is valid. Examples are included.