Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896693 | Journal of Functional Analysis | 2018 | 21 Pages |
Abstract
We show that there exist complete and minimal systems of time-frequency shifts of Gaussians in L2(R) which are not strong Markushevich basis (do not admit the spectral synthesis). In particular, it implies that there is no linear summation method for general Gaussian Gabor expansions. On the other hand we prove that the spectral synthesis for such Gabor systems holds up to one dimensional defect.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anton Baranov, Yurii Belov, Alexander Borichev,