  We define and study Toeplitz operators in the space of Herglotz solutions of
the Helmholtz equation in $R^d$. As the most traditional definition of Toeplitz
operators via Bergman-type projection is not available here, we use an approach
based upon the reproducing kernel nature of the Herglotz space and sesquilinear
forms, which results in a meaningful theory. For two important patterns of
sesquilinear forms we discuss a number of properties, including the uniqueness
of determining the symbols from the operator, the finite rank property, the
conditions for boundedness and compactness, spectral properties, certain
algebraic relations.
