Geodesic
Approximation of M\"untz-Sz\'asz type in weighted spaces
Sbornik. Mathematics, Tome 204 (2013) no. 7, pp. 1028-1055

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

The paper looks at whether a system of exponentials $\exp(-\lambda_nt)$, $\operatorname{Re}\lambda_n>0$, is complete in various function spaces on the half-line $\mathbb R_+$. Wide classes of Banach spaces $E$ and $F$ of functions on $\mathbb R_+$ are described such that this system is complete in $E$ and $F$ simultaneously. A test is established to determine when this system is complete in the weighted spaces $C_0$ and $L^p$ with weight $(1+t)^\alpha$ on $\mathbb R_+$, for $\alpha0$ and $\alpha-1$, respectively. Bibliography: 18 titles.
Keywords: Müntz and Szász theorems, complete system of exponentials, spaces with combined norm, weighted spaces
Mots-clés : Laplace transform. 
@article{SM_2013_204_7_a4,
     author = {A. M. Sedletskii},
     title = {Approximation of {M\"untz-Sz\'asz} type in weighted spaces},
     journal = {Sbornik. Mathematics},
     pages = {1028--1055},
     publisher = {mathdoc},
     volume = {204},
     number = {7},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_7_a4/}
}
TY  - JOUR
AU  - A. M. Sedletskii
TI  - Approximation of M\"untz-Sz\'asz type in weighted spaces
JO  - Sbornik. Mathematics
PY  - 2013
SP  - 1028
EP  - 1055
VL  - 204
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2013_204_7_a4/
LA  - en
ID  - SM_2013_204_7_a4
ER  - 
%0 Journal Article
%A A. M. Sedletskii
%T Approximation of M\"untz-Sz\'asz type in weighted spaces
%J Sbornik. Mathematics
%D 2013
%P 1028-1055
%V 204
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2013_204_7_a4/
%G en
%F SM_2013_204_7_a4
A. M. Sedletskii. Approximation of M\"untz-Sz\'asz type in weighted spaces. Sbornik. Mathematics, Tome 204 (2013) no. 7, pp. 1028-1055. http://geodesic.mathdoc.fr/item/SM_2013_204_7_a4/