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
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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/