• DOI:10.1007/S10114-002-0233-3
• Corpus ID: 121735253

Reproducing Spaces and Localization Operators

@article{Dang2004ReproducingSA,
  title={Reproducing Spaces and Localization
Operators},
  author={Shu Jun Dang and Lizhong Peng},
  journal={Acta Mathematica Sinica},
  year={2004},
  volume={20},
  pages={255-260},
  url={https://api.semanticscholar.org/CorpusID:121735253}
}

• S. Dang, Lizhong Peng
• Published 1 March 2004
• Mathematics
• Acta Mathematica Sinica

AbstractThis paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators $$ T_{n} :L^{2} {\left( R \right)} \to L^{2} {\left( {C,e^{{ - \frac{{{\left| z \right|}^{2} }} {2}}} \frac{{dzd\overline{z} }} {{4\pi i}}} \right)} $$, s.t. $$ T_{n} L^{2} {\left( R \right)} \subseteq L^{2} {\left( {C,e^{{ - \frac{{{\left| z \right|}^{2} }} {2}}} \frac{{dzd\overline{z} }} {{4\pi i}}} \right)} $$ are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing… 

AbstractThis paper, by using of windowed Fourier transform (WFT),
gives a family of embedding operators
$$
T_{n} :L^{2} {\left( R \right)} \to L^{2} {\left( {C,e^{{ - \frac{{{\left| z \right|}^{2} }}
{2}}} \frac{{dzd\overline{z} }}
{{4\pi i}}} \right)}
$$, s.t.
$$
T_{n} L^{2} {\left( R \right)} \subseteq L^{2} {\left( {C,e^{{ - \frac{{{\left| z \right|}^{2} }}
{2}}} \frac{{dzd\overline{z} }}
{{4\pi i}}} \right)}
$$ are reproducing
subspaces (n = 0, Bargmann
Space); and gives a reproducing kernel and an orthonormal basis
(ONB) of TnL2(R). Furthermore, it shows the
orthogonal spaces decomposition of
$$
L^{2} {\left( {C,e^{{ - \frac{{{\left| z \right|}^{2} }}
{2}}} \frac{{dzd\overline{z} }}
{{4\pi i}}} \right)}
$$. 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].