This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the constructi...This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B<sub>3</sub> is the subset of all parameters (a,b) ∈R<sup>2</sup>+ </sub>for which the time-frequency shifts of B<sub>3</sub> along aZ × bZ form a Gabor frame for L<sup>2</sup>(R).展开更多
is not completely clear which elements constitute the frame sets of the B-splines currently,but some considerable results have been obtained.In this paper,firstly,the background of frame set is introduced.Secondly,the...is not completely clear which elements constitute the frame sets of the B-splines currently,but some considerable results have been obtained.In this paper,firstly,the background of frame set is introduced.Secondly,the main progress of the frame sets of the B-splines in the past more than twenty years are reviewed,and particularly the progress for the frame set of the 2 order Bspline and the frame set of the 3 order B-spline are explained,respectively.展开更多
文摘This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B<sub>3</sub> is the subset of all parameters (a,b) ∈R<sup>2</sup>+ </sub>for which the time-frequency shifts of B<sub>3</sub> along aZ × bZ form a Gabor frame for L<sup>2</sup>(R).
基金supported in part by the National Natural Science Foundation of China(Grant No.61471410).
文摘is not completely clear which elements constitute the frame sets of the B-splines currently,but some considerable results have been obtained.In this paper,firstly,the background of frame set is introduced.Secondly,the main progress of the frame sets of the B-splines in the past more than twenty years are reviewed,and particularly the progress for the frame set of the 2 order Bspline and the frame set of the 3 order B-spline are explained,respectively.
