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In his book (Functional Analysis, Wiley, New York, 2002), P. Lax constructs
an explicit representation of the Dirichlet-to-Neumann semigroup, when the
matrix of electrical conductivity is the identity matrix and the domain of the problem
in question is the unit ball in $R^n$. We investigate some representations of Dirichlet-to-
Neumann semigroup for a bounded domain. We show that such a nice explicit
representation as in Lax book, is not possible for any domain except Euclidean
balls. It is interesting that the treatment in dimension 2 is completely different than
other dimensions. Finally, we present a natural and probably the simplest numerical
scheme to calculate this semigroup in full generality by using Chernoff?s theorem.
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