Maximal Cluster Sets of L-Analytic Functions Along Arbitrary Curves

Let Ώ be a domain in the N-dimensional real space, let L be an elliptic differential operator, and let (T_n) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ώ. This paper establishes the existence of a dense linear manifold of L-analytic functions all of whose nonzero members have maximal cluster sets under the action of every T_n along any curve ending at the boundary of Ώ such that its closure does not contain any component of the boundary. The above class contains all partial differentiation operators ∂^α, hence the statement extends earlier results due to Boivin, Gauthier, and Paramonov, and due to the first, third, and fourth authors.