Toeplitz operators on Herglotz wave functions

The space of Herglotz wave functions in R2 consists of all the solutions of the Helmholtz equation that can be represented as the Fourier transform in R2 of a measure supported in the circle and with density in L2(S1). This space has a structure of a Hilbert space with reproducing kernel. The purpose of this article is to study Toeplitz operators with nonnegative radial symbols, defined on this space. We study the symbols defining bounded and compact Toeplitz operators as well as the Toeplitz operators belonging to the Schatten classes sp.