Geodesic
An interpolation problem in the class of entire functions of zero order
Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 233-256

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We obtain two criteria for the solubility of an ordinary free interpolation problem in the class of entire functions of (non-prescribed) finite type with respect to a zero proximate order $\rho(r)$. We impose only one natural restriction on $\rho(r)$ guaranteeing that the class considered consists not only of polynomials. One criterion is stated in terms of the measure determined by the interpolation nodes, and the other in terms of the canonical product generated by these nodes.
Keywords: zero proximate order, free interpolation, interpolation sequence, canonical product, Dirac measure, Nevanlinna counting function. 
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     author = {O. A. Bozhenko and A. F. Grishin and K. G. Malyutin},
     title = {An interpolation problem in the class of entire functions of zero order},
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O. A. Bozhenko; A. F. Grishin; K. G. Malyutin. An interpolation problem in the class of entire functions of zero order. Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 233-256. http://geodesic.mathdoc.fr/item/IM2_2015_79_2_a1/