Geodesic
On the Stability of the Uniform Minimality of a~Set of Exponentials
Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 165-177.

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

Some conditions on sequences $(\lambda_n)$ and $(\mu_n)$ to be nearby are given in order that the corresponding systems of complex exponentials $(\exp(i\lambda_nt))$ and $(\exp(i\mu_nt))$ be simultaneously uniformly minimal in $L^p(-\pi,\pi)$, $1\le p\infty$, and in $C[-\pi,\pi]$. 
@article{CMFD_2007_25_a12,
     author = {A. M. Sedletskii},
     title = {On the {Stability} of the {Uniform} {Minimality} of {a~Set} of {Exponentials}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {165--177},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_25_a12/}
}
TY  - JOUR
AU  - A. M. Sedletskii
TI  - On the Stability of the Uniform Minimality of a~Set of Exponentials
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2007
SP  - 165
EP  - 177
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2007_25_a12/
LA  - ru
ID  - CMFD_2007_25_a12
ER  - 
%0 Journal Article
%A A. M. Sedletskii
%T On the Stability of the Uniform Minimality of a~Set of Exponentials
%J Contemporary Mathematics. Fundamental Directions
%D 2007
%P 165-177
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2007_25_a12/
%G ru
%F CMFD_2007_25_a12
A. M. Sedletskii. On the Stability of the Uniform Minimality of a~Set of Exponentials. Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 165-177. http://geodesic.mathdoc.fr/item/CMFD_2007_25_a12/

[1] Ilin V. A., “Neobkhodimye i dostatochnye usloviya bazisnosti v $L_p$ i ravnoskhodimosti s trigonometricheskim ryadom spektralnykh razlozhenii po sisteme eksponent”, Dokl. AN SSSR, 273:4 (1983), 789–793 | MR

[2] Krein S. G., Funktsionalnyi analiz, Nauka, M., 1972 | MR | Zbl

[3] Milman V. D., “Geometricheskaya teoriya prostranstv Banakha”, UMN, 25:3 (1970), 113–174 | MR

[4] Sedletskii A. M., “Izbytki sistem pokazatelnykh funktsii”, Matem. zametki, 22:6 (1977), 803–814

[5] Sedletskii A. M., “Izbytki sistem eksponentsialnykh funktsii”, Izv. AN SSSR. Ser. matem., 44:1 (1980), 203–218 | MR

[6] Sedletskii A. M., “Izbytki blizkikh sistem eksponent v $L^p$”, Sib. matem. zhurn., 24:4 (1983), 164–175 | MR

[7] Sedletskii A. M., “O chisto mnimykh vozmuscheniyakh pokazatelei $\lambda_n$ v sisteme $\{e^{i\lambda_nt}\}$”, Sib. matem. zhurn., 26:4 (1985), 151–158 | MR

[8] Sedletskii A. M., “Approksimativnye svoistva sistem eksponent v $L^p(a,b)$”, Differents. uravn., 31:10 (1995), 1639–1645 | MR

[9] Sedletskii A. M., “O tselykh funktsiyakh klassa S. N. Bernshteina, ne yavlyayuschikhsya preobrazovaniyami Fure–Stiltesa”, Matem. zametki, 61:3 (1997), 367–380 | MR

[10] Sedletskii A. M., “Ustoichivost klassov finitnykh preobrazovanii Fure”, Integralnye preobrazovaniya i spets. funktsii. Informatsionnyi byulleten, 1, no. 2, Izd-vo VTs RAN, 1997, 17–19

[11] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Mir, M., 1984 | MR

[12] Edvards R., Ryady Fure v sovremennom izlozhenii, T. 2, Mir, M., 1985

[13] Alexander W. O., Redheffer R., “The excess of sets of complex exponentials”, Duke Math. J., 34 (1967), 59–72 | DOI | MR | Zbl

[14] Elsner J., “Zulässige Abänderungen von Exponentialsystemen im $L^p(-A,A)$”, Math. Z., 120 (1971), 211–220 | DOI | MR | Zbl

[15] Redheffer R., “Completeness of sets of complex exponentials”, Adv. Math., 24 (1977), 1–62 | DOI | MR | Zbl

[16] Titchmarsh E. C., “The zeros of certain integral functions”, Proc. London Math. Soc. Ser. 2, 25 (1926), 283–302 | DOI | MR | Zbl

[17] Young R., “On perturbing bases of complex exponentials in $L^2(-\pi,\pi)$”, Proc. Amer. Math. Soc., 53 (1975), 137–140 | DOI | MR | Zbl