Geodesic
Approximation of M\"untz--Szasz type in weighted $L^p$ spaces, and the zeros of functions of the Bergman classes in a half-plane
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 92-100

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

We study the completeness of the system of exponents $\exp(-\lambda_nt)$, $\operatorname{Re}\lambda_n>0$, in spaces $L^p$ with the power weigh on the semiaxis $\mathbb R_+$. We prove a sufficient condition for the completeness; one can treat it as a modification of the well-known Szasz condition. With $p=2$ it is unimprovable (in a sense). The proof is based on the results (which are also obtained in this paper) on the distribution of zeros of functions of the Bergman classes in a halfplane.
Keywords: the Szasz theorem, the completeness of the system of exponents on a semiaxis, Bergman classes, zeros of analytic functions. 
@article{IVM_2008_5_a10,
     author = {A. M. Sedletskii},
     title = {Approximation of {M\"untz--Szasz} type in weighted $L^p$ spaces, and the zeros of functions of the {Bergman} classes in a half-plane},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {92--100},
     publisher = {mathdoc},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_5_a10/}
}
TY  - JOUR
AU  - A. M. Sedletskii
TI  - Approximation of M\"untz--Szasz type in weighted $L^p$ spaces, and the zeros of functions of the Bergman classes in a half-plane
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 92
EP  - 100
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_5_a10/
LA  - ru
ID  - IVM_2008_5_a10
ER  - 
%0 Journal Article
%A A. M. Sedletskii
%T Approximation of M\"untz--Szasz type in weighted $L^p$ spaces, and the zeros of functions of the Bergman classes in a half-plane
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 92-100
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2008_5_a10/
%G ru
%F IVM_2008_5_a10
A. M. Sedletskii. Approximation of M\"untz--Szasz type in weighted $L^p$ spaces, and the zeros of functions of the Bergman classes in a half-plane. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 92-100. http://geodesic.mathdoc.fr/item/IVM_2008_5_a10/