  Unlike in complex linear operator theory, polynomials or, more generally,
Laurent series in antilinear operators cannot be modelled with complex
analysis. There exists a corresponding function space, though, surfacing in
spectral mapping theorems. These spectral mapping theorems are inclusive in
general. Equality can be established in the self-adjoint case. The arising
functions are shown to possess a biradial character. It is shown that to any
given set of Jacobi parameters corresponds a biradial measure yielding these
parameters in an iterative orthogonalization process in this function space,
once equipped with the corresponding $L^2$ structure.
