Computational Methods and Function Theory 9 (2009), No. 1, 111--125
Copyright Heldermann Verlag 2009
Erik Lundberg
elundber@mail.usf.edu , University of South Florida, Mathematics, 4202 E. Fowler Ave., PHY114, Tampa FL 33617, U.S.A.
We consider the Dirichlet problem in the plane with entire data on algebraic curves. More specifically we will be interested in where singularities develop when a solution is continued analytically. Our approach relies on the annihilator method from functional analysis. The annihilating measures are supported on finite sets called lightning bolts.
Keywords: Entire data, algebraic curve, lightning bolt, singularity, analytic continuation, approximation by superpositions.
MSC 2000: Primary 30E25; Secondary 35J25.
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