Reproducing Spaces and Localization Operators

This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators Tn:L2(R)L2(C,e|z|22dzdz4i), s.t. TnL2(R)L2(C,e|z|22dzdz4i) are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of T n L 2(R). Furthermore, it shows the orthogonal spaces decomposition of L2(C,e|z|22dzdz4i). Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6].