In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In additio...In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.展开更多
We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncert...We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncertainty principle and Matolcsi-Sz^ics uncertainty principle.展开更多
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Supported by the National Natural Science Foundation of China(Grant No.11271092)the Natural Science Foundation of Guangdong Province(Grant No.S2011010005367)
文摘In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.
文摘We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncertainty principle and Matolcsi-Sz^ics uncertainty principle.
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。
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].
