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Identification of operators with bandlimited symbols. (English) Zbl 1141.42020

Underspread and overspread operators are time-varying Hilbert-Schmidt operators acting on a space of \(d\)-dimensional signals. The corresponding kernels are \(2d\)-dimensional. The operator can be identified based on observations of its action on a specified signal, together with the knowledge that the operator belongs to a special class. In the paper, a classical conjecture concerning the necessity of the underspread condition for the identifiability of certain operator classes is proved.

MSC:

42C15 General harmonic expansions, frames
47G10 Integral operators
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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