Geodesic
Approximation of Müntz–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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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{\textendash}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},
     year = {2008},
     number = {5},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2008_5_a10/}
}
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A. M. Sedletskii. Approximation of Müntz–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/

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