Maximal cluster sets of L-analytic functions along arbitrary curves

Let Ω be a domain in the N -dimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ω. It is proved in this paper 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 Tn along any curve ending at the boundary of Ω such that its ω-limit 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 to the first, third and fourth authors. 2000 Mathematics Subject Classification: Primary 30D40. Secondary 30E10, 31B35, 41A30, 47F05.