Abstract
Let Ώ be a domain in the N-dimensional real space, let L be an elliptic differential operator, and let (Tn) 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 Tn 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.
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Bernal-Gonzalez, L., Bonilla, A., Calderon-Moreno, M. et al. Maximal Cluster Sets of L-Analytic Functions Along Arbitrary Curves. Constr Approx 25, 211–219 (2007). https://doi.org/10.1007/s00365-006-0636-5
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DOI: https://doi.org/10.1007/s00365-006-0636-5