Geodesic
Lower Bounds for Positive and Negative Parts of Measures and the Arrangement of Singularities of Their Laplace Transforms
Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 84-98

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

For a real measure with variation $V(x)$ satisfying the estimate $V(x)\le c_0\exp(Cx)$ and with the Laplace transform holomorphic in the disk $\{|s-C|\le C\}$ and having at least one pole of order $m$, we obtain lower bounds for the positive and negative parts of the measure $V_\pm(x)>cx^m$, $x>x_0$. We establish lower bounds for $V_\pm(x)$ on “short” intervals. Applications to number theory of the results obtained are considered.
Keywords: real measure, positive and negative parts of a measure, analytic function, pole of a meromorphic function, Möbius function, Riemann zeta function.
Mots-clés : Laplace transform 
@article{MZM_2007_82_1_a9,
     author = {A. Yu. Popov and A. P. Solodov},
     title = {Lower {Bounds} for {Positive} and {Negative} {Parts} of {Measures} and the {Arrangement} of {Singularities} of {Their} {Laplace} {Transforms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {84--98},
     publisher = {mathdoc},
     volume = {82},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a9/}
}
TY  - JOUR
AU  - A. Yu. Popov
AU  - A. P. Solodov
TI  - Lower Bounds for Positive and Negative Parts of Measures and the Arrangement of Singularities of Their Laplace Transforms
JO  - Matematičeskie zametki
PY  - 2007
SP  - 84
EP  - 98
VL  - 82
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a9/
LA  - ru
ID  - MZM_2007_82_1_a9
ER  - 
%0 Journal Article
%A A. Yu. Popov
%A A. P. Solodov
%T Lower Bounds for Positive and Negative Parts of Measures and the Arrangement of Singularities of Their Laplace Transforms
%J Matematičeskie zametki
%D 2007
%P 84-98
%V 82
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a9/
%G ru
%F MZM_2007_82_1_a9
A. Yu. Popov; A. P. Solodov. Lower Bounds for Positive and Negative Parts of Measures and the Arrangement of Singularities of Their Laplace Transforms. Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 84-98. http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a9/