A quasianalyticity property for monogenic solutions of small divisor problems

We discuss the quasianalytic properties of various spaces of functions suit-able for one-dimensional small divisor problems. These spaces are formed of functions [inline-graphic not available: see fulltext]1-holomorphic on certain compact sets Kj of the Riemann sphere (in the Whitney sense), as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of Kj with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity). It turns out that a kind of generalized analytic continuation through the unit circle is possible under suitable conditions on the Kj’s.