Geodesic
Theorems of Paley--Wiener and M\"untz--Sz\'asz type
Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 821-847

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In the paper a new integral representation of the well-known function classes $\mathscr H_2[\alpha]$ ($0\alpha1$) is established, which in the limiting case $\alpha=1$ goes into the Paley–Wiener theorem. A Hilbert space metric is introduced into the classes $\mathscr H_2[\alpha]$ ($0\alpha+\infty$), and a criterion for closedness of certain systems of functions in these spaces is established. In particular, a theorem of Müntz–Szász type in the complex domain is proved, and a complete intrinsic description is given of the corresponding nonclosed systems. Bibliography: 9 titles. 
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     author = {M. M. Dzhrbashyan and V. M. Martirosyan},
     title = {Theorems of {Paley--Wiener} and {M\"untz--Sz\'asz} type},
     journal = {Izvestiya. Mathematics },
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M. M. Dzhrbashyan; V. M. Martirosyan. Theorems of Paley--Wiener and M\"untz--Sz\'asz type. Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 821-847. http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a6/