| I consider the relationship between Gabor-Daubechies windowed Fourier localization operators Lw4 [12, 13, 14, 15, 16, 17] and Berezin-Toeplitz operators T4 [2, 3, 4, 5, 6, 7, 8, 11, 20, 22], using the Bargmann isometry b ([1]; [18], pp. 40, 47). This analysis is based on some papers by L. A. Coburn [8, 9, 10].; For "window" w a finite linear combination of Hermite functions, and some interesting classes of "symbols" 4 , Coburn conjectured an equivalence of the form bLw4b-1 =C*M4C=TI+D 4 where C is a precisely determined operator, and D is a constant-coefficient linear, differential operator with constant term 0.; I settled Coburn's conjecture affirmatively by obtaining the exact formulas for C and the linear differential operator D. In addition, I extended the conjectured result to a very general class of functions 4 . This analysis permits the extension of results which were known for w = w0, the normalized Gaussian, to considerably more general windows. |
