This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB)...This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. 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 . 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].展开更多
基金Research supported by 973 Project G1999075105 and NNFS of China,Nos.90104004 and 69735020
文摘This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. 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 . 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].
基金Supported by NSFC(No.12001482)Innovative Guidance Project of Science and Technology of Zhaoqing City(Nos.202004031503,202004031505)+2 种基金Scientific Research Ability Enhancement Program for Excellent Young Teachers of Zhaoqing University(No.ZQ202108)Natural Research Project of Zhaoqing University(Nos.221622,KY202141,201910)Innovative Research Team Project of Zhaoqing University。
