Characterizing images of standard Hilbert spaces of holomorphic functions by means of some special integral transforms is a well-studied classical problem. The present paper deals with a similar problem for the weighted singular Cauchy integral transform \(\cal{C}_\mu\) acting on the special class of poly-analytic functions on the complex plane, a generalization of holomorphic ones and arising as L2-eigenspaces of the magnetic Laplacian. In fact, we provide a concrete characterization of the action of \(\cal{C}_\mu\) on the poly-analytic and anti-polyanalytic Bargmann spaces of Gaussian functions. We moreover describe the range of the local operators arising as the product with the m-Bergman projection on the poly-Bargmann spaces, which together form an orthogonal Hilbertian decomposition of the underlying Hilbert space.
