Geodesic
A~Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum
Informatics and Automation, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 94-101.

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

A new lower estimate of the $L_1$ norm of a general exponential sum is established in terms of the ratios of the $L_p$ ($p>2$) and $L_2$ norms of dyadic blocks. In particular, for sums of exponents with coefficients whose absolute values are 0 and 1, the estimates are found such that the density and arithmetic properties of the spectrum are simultaneously taken into account. The results obtained are unimprovable in a certain sense. 
@article{TRSPY_2001_232_a9,
     author = {S. V. Bochkarev},
     title = {A~Method for {Estimating} the $L_1$ {Norm} of an {Exponential} {Sum} {Based} on {Arithmetic} {Properties} of the {Spectrum}},
     journal = {Informatics and Automation},
     pages = {94--101},
     publisher = {mathdoc},
     volume = {232},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a9/}
}
TY  - JOUR
AU  - S. V. Bochkarev
TI  - A~Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum
JO  - Informatics and Automation
PY  - 2001
SP  - 94
EP  - 101
VL  - 232
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a9/
LA  - ru
ID  - TRSPY_2001_232_a9
ER  - 
%0 Journal Article
%A S. V. Bochkarev
%T A~Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum
%J Informatics and Automation
%D 2001
%P 94-101
%V 232
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a9/
%G ru
%F TRSPY_2001_232_a9
S. V. Bochkarev. A~Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum. Informatics and Automation, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 94-101. http://geodesic.mathdoc.fr/item/TRSPY_2001_232_a9/

[1] Zigmund A., Trigonometricheskie ryady, T. 1, 2, Mir, M., 1965 | MR

[2] Garnett Dzh., Ogranichennye analiticheskie funktsi, Mir, M., 1984 | MR | Zbl

[3] Bochkarev S. V., “Ryady Valle Pussena v prostranstvakh BMO, $L_1$ i $H^1(D)$ i multiplikativnye neravenstva”, Tr. MIAN, 210, 1995, 41–64 | MR | Zbl

[4] Bochkarev S. V., “Ob odnom metode otsenki $L_1$-normy eksponentsialnoi summy”, Tr. MIAN, 218, 1997, 74–76 | MR | Zbl

[5] Bochkarev S. V., “Multiplikativnye otsenki $L_1$-normy eksponentsialnykh summ”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Izd-vo AFTs, M., 1999, 57–68 | MR