Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 20, pp. 1-10.

On a generalized reflection law for functions satisfying the Helmholtz equation

Dawit Aberra

We investigate a generalized point to point reflection law for the solutions of the Helmholtz equation in two independent variables, obtaining results that include some previously known results of Khavinson and Shapiro as special cases. As a consequence, we obtain partial negative answers to the ``point to compact set reflection'' conjecture suggested by Garabedian and others.

Submitted October 9, 1998. Published June 4, 1999.
Math Subject Classification: 31A05, 31A35, 31B05
Key Words: Reflection law, Helmholtz operator.

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Dawit Aberra
Department of Mathematical Sciences, University of Arkansas
Fayetteville, AR 72701, USA
e-mail: daberra@comp.uark.edu
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