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We discuss the quasianalytic properties of various spaces of functionssuitable for one-dimensional small divisor problems. These spaces are formed offunctions C^1-holomorphic on certain compact sets K_j of the Riemann sphere (inthe Whitney sense), as is the solution of a linear or non-linear small divisorproblem when viewed as a function of the multiplier (the intersection of K_jwith the unit circle is defined by a Diophantine-type condition, so as to avoidthe divergence caused by roots of unity). It turns out that a kind ofgeneralized analytic continuation through the unit circle is possible undersuitable conditions on the K_j's.

A quasianalyticity property for monogenic solutions of small divisor problems