Abstract
Conversely, if a solution ir(s) of (4) admits a power-series expansion (2) with non-negative coefficients, then the 7rj form a stationary measure. Harris has conjectured that the stationary measure for any Galton-Watson process is unique up to a constant multiplicative factor, or, equivalently, that there is exactly one stationary measure satisfying (3). The purpose of this note is to provide a counterexample to this conjecture. Let w be any entire function, not identically zero, which has period 1, and satisfies co(0) = 0. It follows from a well-known property of the equation (4) first noticed by Abel (cf. [1, ?11.4]) that, if {ir1} is a
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