Boundary values of zero solutions of hypoelliptic differential operators in ultradistribution spaces (Q6046111)

This paper deals with ultradistributional boundary values of zero solutions of hypoelliptic constant coefficients partial differential operators \(P(D)\) on \(\mathbb R^{d+1}\). In particular, given two open sets \(X\subseteq \mathbb R^d\) and \(V\subset\mathbb R^{d+1}\) with \(V\cap\mathbb R^d=X\), the authors characterize \(C^\infty\) functions \(f\) on \(V\setminus X\) satisfying \(P(D)f=0\) that admit a boundary value as a Gevrey ultradistribution on \(X\) (both Beurling and Roumieu cases), in terms of their local growth properties near \(X\).