We consider the problem of maximizing the time-frequency concentration of a square-integrable function on a given subset of the phase space. In this setting, concentration is measured by the localized Lebesgue norm of a nonlinear time-frequency representation, such as the ambiguity transform or the Wigner distribution. We discuss recent results on the matter, showing the existence of concentration maximizers by means of a concentration-compactness approach and a number of interesting technical findings.
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