Geodesic
M\"untz--Sz\'asz~type
Izvestiya. Mathematics , Tome 70 (2006) no. 5, pp. 1031-1050

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We consider the problem of completeness of the system of exponentials $\exp\{-\lambda_nt\}$, $\operatorname{Re}\lambda_n>0$, in direct products $E=E_1\times E_2$ of the spaces $E_1=E_1(0,1)$ and $E_2=E_2(1,\infty)$ of functions defined on $(0,1)$ and $(1,\infty)$, respectively. We describe rather broad classes of spaces $E_1$ and $E_2$ such that the well-known condition of Szász is necessary for the completeness of the above system in $E$ and sufficient for this completeness. 
@article{IM2_2006_70_5_a7,
     author = {A. M. Sedletskii},
     title = {M\"untz--Sz\'asz~type},
     journal = {Izvestiya. Mathematics },
     pages = {1031--1050},
     publisher = {mathdoc},
     volume = {70},
     number = {5},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_5_a7/}
}
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A. M. Sedletskii. M\"untz--Sz\'asz~type. Izvestiya. Mathematics , Tome 70 (2006) no. 5, pp. 1031-1050. http://geodesic.mathdoc.fr/item/IM2_2006_70_5_a7/