Abstract
Recent work of Pavlov suggests the following definition: positive integers p1< p2<…form an interpolation sequence if a certain kind of interpolation problem on the sequence always has a solution in a class of entire functions of restricted growth, corresponding to order one, convergence type. We call a set of powers { z pn } strongly nonspanning if the approximation, by linear combinations, to positive integral powers not in the sequence is uniformly bad for all curves extending from one circle about the origin to another; there is a related notion of strongly free sets. It is shown that for an interpolation sequence, the corresponding powers are strongly free and strongly nonspanning. As one corollary (implicit in Pavlov's work), an interpolation sequence { p n } is a Macintyre sequence: a non-constant entire function Σa nz pn can not be bounded on a curve going to infinity. Our interpolation sequences include the sequences of exponents which Kövari and Pavlov have identified as Macintyre sequences.
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