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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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/

[1] A. A. Gol'dberg, B. Ya. Levin, I. V. Ostrovkij, “Entire and meromorphic functions”, Complex analysis, I, Encyclopaedia Math. Sci., 85, Springer, Berlin, 1995, 1–193 | DOI | MR | MR | Zbl | Zbl

[2] A. V. Bratishchev, Yu. F. Korobeinik, “The multiple interpolation problem in the space of entire functions of given proximate order”, Math. USSR-Izv., 10:5 (1976), 1049–1074 | DOI | MR | Zbl

[3] B. Ja. Levin, Distribution of zeros of entire functions, Amer. Math. Soc., Providence, R.I., 1964, viii+493 pp. | MR | MR | Zbl | Zbl

[4] N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular variation, Encyclopedia Math. Appl., 27, Cambridge Univ. Press, Cambridge, 1987, xx+491 pp. | DOI | MR | Zbl

[5] A. F. Grishin, T. I. Malyutina, “Ob utochnennom poryadke”, Kompleksnyi analiz i matematicheskaya fizika, Krasnoyarskii gos. un-t, Krasnoyarsk, 1998, 10–24

[6] A. F. Grishin, I. V. Poedintseva, “Abelevy i tauberovy teoremy dlya integralov”, Algebra i analiz, 26:3 (2014), 1–88

[7] K. G. Malyutin, Interpolyatsiya golomorfnymi funktsiyami, Dis. $\dots$ kand. fiz.-matem. nauk, Kharkovskii gos. un-t im. A. M. Gorkogo, Kharkov, 1980, 104 pp.

[8] A. A. Gol'dberg, N. V. Zabolotskii, “Concentration index of a subharmonic function of zeroth order”, Math. Notes, 34:2 (1983), 596–601 | DOI | MR | Zbl

[9] K. G. Malyutin, O. A. Bozhenko, “Weakly regular sets”, \"{I}stanb. Univ. Sci. Fac. J. Math. Phys. Astronom., 4 (2013), 1–8 | MR