Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Summability properties of Gabor expansions. / Baranov, Anton; Belov, Yurii; Borichev, Alexander.
в: Journal of Functional Analysis, Том 274, № 9, 01.05.2018, стр. 2532-2552.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Summability properties of Gabor expansions
AU - Baranov, Anton
AU - Belov, Yurii
AU - Borichev, Alexander
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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.
AB - 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.
KW - Complete and minimal systems
KW - Fock spaces
KW - Gabor systems
KW - Spectral synthesis
KW - INTERPOLATION
KW - DENSITY THEOREMS
KW - BARGMANN-FOCK SPACE
UR - http://www.scopus.com/inward/record.url?scp=85039857536&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2017.12.009
DO - 10.1016/j.jfa.2017.12.009
M3 - Article
AN - SCOPUS:85039857536
VL - 274
SP - 2532
EP - 2552
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 9
ER -
ID: 32722401