J Austral Math Soc Ser A 54 pp263--286, 1993.

Gevrey Spaces and Their Intersections

A. F. M. Ter Elst

Abstract

For unbounded operators A₁, ..., A_d, Gevrey spaces S_l1,...,ld(A₁, ..., A_d) of order (l₁, ..., l_d) are introduced, where the orders l₁, ..., l_d need not be equal. These extend the notion of Gevrey space defined by Goodman and Wallach where l₁ = ... = l_d. Several mild conditions on the operators A₁, ..., A_d and the orders l₁, ..., l_d are presented such that the equality S_l1,...,ld(A₁, ..., A_d) = Ç^d_k=1 S_lk(A_k) is valid. Examples are included.

1991 AMS Subject Classification: 47D30, 22E45

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Authors

A. F. M. Ter Elst

Department of Mathematics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.