On approximations by shifts of the Gaussian function
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
math.CA↗
arXiv subjects
Gerard Ascensi
Publications and source records attributed to Gerard Ascensi.
Phase space distribution of Gabor expansions
We present an example of a complete and minimal Gabor system consisting of time-frequency shifts of a Gaussian, localized at the coordinate axes in the time-frequency plane (phase space). Asymptotically, the number of time-frequency shifts contained in a disk centered at the origin is only 2/pi times the number of points from the von Neumann lattice found in the same disk. Requiring a certain regular distribution in phase space, we show that our system has minimal density among all complete and minimal systems of time-frequency shifts of a Gaussian.
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Poisson type generators for L^1(R)
We characterize the discrete sets L of the real line such that {f(t-l), l in L} span L^1(R), f being an L^1(R)-function whose Fourier transform behaves like the one of the Poisson function.
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Model spaces results for the Gabor and Wavelet transforms
We prove that the unique Gabor atom with analytical model space is the Gaussian function. We give an analogous result for the wavelet transform. For the general case we give a new approach to study the irregular Gabor and wavelet frames. We improve some results for Gabor atoms in the Feichtinger algebra, and for a special class of wavelets.
math.FA↗