Pseudoinverses in the Hardy space of the polydisk

The methods of least-squares approximation have been used in many areas of engineering since the later half of the 20th century — in particular, in 2D recursive digital filter design, where electrical engineers manipulate polynomials of two complex variables to control the output of a 2D signal. Difficulties arise due to limited factorization results for polynomials in several variables, which motivates a more abstract approach. This talk presents an operator-theoretic method for studying these polynomials via the pseudoinverse of an associated operator, recovers some previously known results easily within the framework, and — to maintain flexibility with the engineering applications — presents most results in the d-dimensional case.

Further reading: Bénéteau–Centner survey (arXiv:2102.01725).