CHARACTERIZATION OF THE ω-HYPOELLIPTIC CONVOLUTION OPERATORS ON ULTRADISTRIBUTIONS

Abstract. We achieve characterizations of those ultradistributions µ ∈ E ′(ω)(RN) (resp. E ′{ω}(R N) ) with compact support such that for each ultradifferentiable function f in E(ω)(R N) (resp. in E{ω}(RN) ) each solution ν ∈ D ′(ω)(RN) (resp. in D ′{ω}(RN) ) of the convolution equation µ ∗ ν = f belongs to the same class as f. These characterizations extend classical results of Ehrenpreis and Hörmander for distributions and Björck and Chou for ultradistributions