\(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory
In this 54-page-paper, the author considers the so-called \(k\)-Hankel Gabor transform on \({\mathbb R}^d\) with radial windows. He presents the fundamental properties of the Moore-Penrose inverses and reproducing kernels in the \(k\)-Hankel Gabor transform setting, which naturally generate certain applications of the general theory of reproducing kernels to Tikhonov regularization, and also the best approximation of the \(k\)-Hankel Gabor transform on associated generalized Sobolev spaces. Uncertainty principles involving time-frequency representations are also considered as applications of the \(k\)-Hankel Gabor transform. Moreover, time-frequency localization operators are studied, and the spectrogram associated with the \(k\)-Hankel Gabor transform is analysed.
scientific article; zbMATH DE number 7352432
scientific article