Standard

Summability properties of Gabor expansions. / Baranov, Anton; Belov, Yurii; Borichev, Alexander.

In: Journal of Functional Analysis, Vol. 274, No. 9, 01.05.2018, p. 2532-2552.

Research output: Contribution to journal › Article › peer-review

Harvard

Baranov, A, Belov, Y & Borichev, A 2018, 'Summability properties of Gabor expansions', Journal of Functional Analysis, vol. 274, no. 9, pp. 2532-2552. https://doi.org/10.1016/j.jfa.2017.12.009

APA

Baranov, A., Belov, Y., & Borichev, A. (2018). Summability properties of Gabor expansions. Journal of Functional Analysis, 274(9), 2532-2552. https://doi.org/10.1016/j.jfa.2017.12.009

Vancouver

Baranov A, Belov Y, Borichev A. Summability properties of Gabor expansions. Journal of Functional Analysis. 2018 May 1;274(9):2532-2552. https://doi.org/10.1016/j.jfa.2017.12.009

Author

Baranov, Anton ; Belov, Yurii ; Borichev, Alexander. / Summability properties of Gabor expansions. In: Journal of Functional Analysis. 2018 ; Vol. 274, No. 9. pp. 2532-2552.

BibTeX

@article{3434f69c18ba4d63b2cd38f728709f70,
title = "Summability properties of Gabor expansions",
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.",
keywords = "Complete and minimal systems, Fock spaces, Gabor systems, Spectral synthesis, INTERPOLATION, DENSITY THEOREMS, BARGMANN-FOCK SPACE",
author = "Anton Baranov and Yurii Belov and Alexander Borichev",
year = "2018",
month = may,
day = "1",
doi = "10.1016/j.jfa.2017.12.009",
language = "English",
volume = "274",
pages = "2532--2552",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Elsevier",
number = "9",

}

RIS

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