Function Spaces of Polyanalytic Functions

This article is meant as both an introduction and a review of some of the recent developments on Fock and Bergman spaces of polyanalytic functions. The study of polyanalytic functions is a classic topic in complex analysis. However, thanks to the interdisciplinary transference of knowledge promoted within the activities of HCAA network it has benefited from a cross-fertilization with ideas from signal analysis, quantum physics, and random matrices. We provide a brief introduction to those ideas and describe some of the results of the mentioned cross-fertilization. The departure point of our investigations is a thought experiment related to a classical problem of multiplexing of signals, in order words, how to send several signals simultaneously using a single channel.

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