A few remarks on sampling of signals with small spectrum
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Orthogonal series, approximation theory, and related problems, Tome 280 (2013), pp. 247-254.

Voir la notice de l'article provenant de la source Math-Net.Ru

Given a bounded set $S$ of small measure, we discuss the existence of sampling sequences for the Paley–Wiener space $\mathrm {PW}_S$, which have both densities and sampling bounds close to the optimal ones.
@article{TM_2013_280_a16,
     author = {Shahaf Nitzan and Alexander Olevskii and Alexander Ulanovskii},
     title = {A few remarks on sampling of signals with small spectrum},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {247--254},
     publisher = {mathdoc},
     volume = {280},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_280_a16/}
}
TY  - JOUR
AU  - Shahaf Nitzan
AU  - Alexander Olevskii
AU  - Alexander Ulanovskii
TI  - A few remarks on sampling of signals with small spectrum
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2013
SP  - 247
EP  - 254
VL  - 280
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2013_280_a16/
LA  - en
ID  - TM_2013_280_a16
ER  - 
%0 Journal Article
%A Shahaf Nitzan
%A Alexander Olevskii
%A Alexander Ulanovskii
%T A few remarks on sampling of signals with small spectrum
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2013
%P 247-254
%V 280
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2013_280_a16/
%G en
%F TM_2013_280_a16
Shahaf Nitzan; Alexander Olevskii; Alexander Ulanovskii. A few remarks on sampling of signals with small spectrum. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Orthogonal series, approximation theory, and related problems, Tome 280 (2013), pp. 247-254. http://geodesic.mathdoc.fr/item/TM_2013_280_a16/

[1] Batson J.D., Spielman D.A., Srivastava N., “Twice-Ramanujan sparsifiers”, Proc. 41st annual ACM symposium on theory of computing (STOC 2009), ACM, New York, 2009, 255–262, arXiv: 0808.0163 [cs.DS] | DOI | MR

[2] Bourgain J., Tzafriri L., “Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis”, Isr. J. Math., 57:2 (1987), 137–224 | DOI | MR | Zbl

[3] Bourgain J., Tzafriri L., “On a problem of Kadison and Singer”, J. reine angew. Math., 420 (1991), 1–43 | MR | Zbl

[4] Casazza P.G., Tremain J.C., “The Kadison–Singer problem in mathematics and engineering”, Proc. Natl. Acad. Sci. USA, 103:7 (2006), 2032–2039 | DOI | MR | Zbl

[5] Kashin B.S., “Ob odnom svoistve bilineinykh form”, Soobsch. AN GruzSSR, 97:1 (1980), 29–32 | MR | Zbl

[6] Kashin B.S., “Some properties of matrices of bounded operators from space $l^n_2$ to $l^m_2$”, Sov. J. Contemp. Math. Anal., Arm. Acad. Sci., 15:5 (1980), 44–57 | MR | Zbl | Zbl

[7] Kashin B.S., Tzafriri L., Some remarks on the restriction of operators to coordinate subspaces, Preprint, Hebrew Univ. Jerusalem, 1994 | MR | Zbl

[8] Landau H.J., “Necessary density conditions for sampling and interpolation of certain entire functions”, Acta math., 117 (1967), 37–52 | DOI | MR | Zbl

[9] Lawton W., “Minimal sequences and the Kadison–Singer problem”, Bull. Malays. Math. Sci. Soc. Ser. 2, 33:2 (2010), 169–176 | MR | Zbl

[10] Lunin A.A., “Operator norms of submatrices”, Math. Notes, 45 (1989), 248–252 | DOI | MR | Zbl

[11] Matei B., Meyer Y., “A variant of compressed sensing”, Rev. mat. Iberoamer., 25:2 (2009), 669–692 | DOI | MR | Zbl

[12] OlevskiĭA., Ulanovskii A., “Universal sampling and interpolation of band-limited signals”, Geom. Funct. Anal., 18:3 (2008), 1029–1052 | DOI | MR | Zbl

[13] Ruzsa I.Z., “On difference sets”, Stud. sci. math. Hung., 13 (1978), 319–326 | MR | Zbl

[14] Spielman D.A., Srivastava N., An elementary proof of the restricted invertibility theorem, E-print, 2009, arXiv: 0911.1114 [math.FA] | MR | Zbl

[15] Vershynin R., Coordinate restrictions of linear operators in $l_2^n$, E-print, 2000, arXiv: math/0011232 [math.FA]