"Daubechies-type theorems for projective and mixed-state localization operators with Hagedorn windows."Svela, ErlingWe use a method of moments to examine the eigenvalue problem for time-frequency localization operators. This method yields extensions of Daubechies' classical theorem to a larger class of window functions, namely Hagedorn wavepackets. In higher dimensions we will discuss localization on symplectic Reinhardt domains, and discuss how these domains appear in practice. Through the connection to the STFT-localization problem, we will also discuss a novel geometric interpretation of certain weighted localization operators as localization on projective space. With the above results in mind, we will also construct a class of quantum states such that the solution to the eigenvalue problem of mixed-state localization operators is given by a Daubechies-type theorem. |
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