Erling Svela - A large sieve principle for the operator STFT with applications to Cohen's class

This talk was part of the Workshop on "Quantum Harmonic Analysis" held at the ESI May 5 - 10, 2025. The large sieve principle, originally a tool from analytic number theory, has been extended and applied to many other areas of analysis. Time-frequency analogues of the large sieve principle have been established for bandlimited functions and for the short-time Fourier transform. At their core, they are statements about the concentration of a signal, or its STFT, and are valuable tools in the study of sparsely concentrated signals. In this talk, we establish a quantum analogue of the STFT large sieve principle, that both works on functions and operators. The principle relies on various tools from quantum harmonic analysis. We will also discuss applications to Cohen's class distributions and recovery of operators. This is joint work with Daniel Abreu and Michael Speckbacher.