  The bijectivity of the mapping, which is represented as expectation, from a
family of Gaussian measures parametrized by linear combinations of Dirac
measures to the space of classical reflectionless potentials is shown. It is
also shown that the bijectivity extends to the space of generalized
reflectionless potentials, which was used by V. Marchenko to study the Cauchy
problem for the KdV equation. In the extension, the stochastic calculus based
on the Brownian sheet plays a key role.
