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k -Hankel Gabor Transform on $$\mathbb {R}^{d}$$ R d and Its Applications to the Reproducing Kernel Theory
Complex Analysis and Operator Theory ( IF 0.7 ) Pub Date : 2021-01-04 , DOI: 10.1007/s11785-020-01042-x Hatem Mejjaoli
中文翻译:
$$ \ mathbb {R} ^ {d} $$ R d上的k -Hankel Gabor变换及其在再现核理论中的应用
更新日期:2021-01-05
Complex Analysis and Operator Theory ( IF 0.7 ) Pub Date : 2021-01-04 , DOI: 10.1007/s11785-020-01042-x Hatem Mejjaoli
In this paper, we introduce and we study the k-Hankel Gabor transform on \(\mathbb {R}^{d}\) with radial windows. We investigate for this transform the general theory of reproducing kernels theory. In particular we study some time–frequency concentration problems and we give some applications of the Tikhonov regularization on the generalized Sobolev spaces.
中文翻译:
$$ \ mathbb {R} ^ {d} $$ R d上的k -Hankel Gabor变换及其在再现核理论中的应用
在本文中,我们介绍并研究了带有径向窗口的\(\ mathbb {R} ^ {d} \)上的k -Hankel Gabor变换。为此,我们研究了繁殖核理论的一般理论。特别是,我们研究了一些时频集中问题,并给出了Tikhonov正则化在广义Sobolev空间上的一些应用。